LMFDB - Embedded newform 80.2.s.b.27.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(3,80)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("80.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.2
Root			$0.0376504 - 1.41371i$ of defining polynomial
Character	$\chi$	$=$	80.27
Dual form			80.2.s.b.3.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29924 - 0.558542i) q^{2} -2.55161 q^{3} +(1.37606 + 1.45136i) q^{4} +(1.49107 + 1.66635i) q^{5} +(3.31516 + 1.42518i) q^{6} +(2.40368 + 2.40368i) q^{7} +(-0.977191 - 2.65426i) q^{8} +3.51070 q^{9} +O(q^{10})$	\(q+(-1.29924 - 0.558542i) q^{2} -2.55161 q^{3} +(1.37606 + 1.45136i) q^{4} +(1.49107 + 1.66635i) q^{5} +(3.31516 + 1.42518i) q^{6} +(2.40368 + 2.40368i) q^{7} +(-0.977191 - 2.65426i) q^{8} +3.51070 q^{9} +(-1.00653 - 2.99782i) q^{10} +(-2.67707 + 2.67707i) q^{11} +(-3.51117 - 3.70331i) q^{12} +2.40164i q^{13} +(-1.78040 - 4.46551i) q^{14} +(-3.80462 - 4.25187i) q^{15} +(-0.212908 + 3.99433i) q^{16} +(-0.0750544 - 0.0750544i) q^{17} +(-4.56125 - 1.96087i) q^{18} +(2.67236 - 2.67236i) q^{19} +(-0.366678 + 4.45708i) q^{20} +(-6.13324 - 6.13324i) q^{21} +(4.97342 - 1.98291i) q^{22} +(2.12375 - 2.12375i) q^{23} +(2.49341 + 6.77263i) q^{24} +(-0.553442 + 4.96928i) q^{25} +(1.34141 - 3.12031i) q^{26} -1.30310 q^{27} +(-0.180999 + 6.79621i) q^{28} +(-3.95795 - 3.95795i) q^{29} +(2.56827 + 7.64925i) q^{30} -1.65367i q^{31} +(2.50762 - 5.07068i) q^{32} +(6.83083 - 6.83083i) q^{33} +(0.0555929 + 0.139435i) q^{34} +(-0.421324 + 7.58941i) q^{35} +(4.83094 + 5.09530i) q^{36} -2.53082i q^{37} +(-4.96467 + 1.97942i) q^{38} -6.12803i q^{39} +(2.96587 - 5.58602i) q^{40} +1.70882i q^{41} +(4.54289 + 11.3942i) q^{42} +3.84601i q^{43} +(-7.56921 - 0.201586i) q^{44} +(5.23469 + 5.85005i) q^{45} +(-3.94547 + 1.57306i) q^{46} +(2.15264 - 2.15264i) q^{47} +(0.543256 - 10.1920i) q^{48} +4.55532i q^{49} +(3.49460 - 6.14717i) q^{50} +(0.191509 + 0.191509i) q^{51} +(-3.48565 + 3.30480i) q^{52} -1.29475 q^{53} +(1.69305 + 0.727839i) q^{54} +(-8.45262 - 0.469246i) q^{55} +(4.03113 - 8.72883i) q^{56} +(-6.81881 + 6.81881i) q^{57} +(2.93166 + 7.35302i) q^{58} +(5.29614 + 5.29614i) q^{59} +(0.935619 - 11.3727i) q^{60} +(10.2413 - 10.2413i) q^{61} +(-0.923645 + 2.14852i) q^{62} +(8.43858 + 8.43858i) q^{63} +(-6.09020 + 5.18744i) q^{64} +(-4.00197 + 3.58100i) q^{65} +(-12.6902 + 5.05960i) q^{66} -10.6230i q^{67} +(0.00565167 - 0.212211i) q^{68} +(-5.41898 + 5.41898i) q^{69} +(4.78640 - 9.62515i) q^{70} +2.27322 q^{71} +(-3.43062 - 9.31831i) q^{72} +(-9.99096 - 9.99096i) q^{73} +(-1.41357 + 3.28815i) q^{74} +(1.41217 - 12.6796i) q^{75} +(7.55589 + 0.201231i) q^{76} -12.8696 q^{77} +(-3.42276 + 7.96180i) q^{78} -8.70617 q^{79} +(-6.97341 + 5.60103i) q^{80} -7.20709 q^{81} +(0.954448 - 2.22017i) q^{82} +11.1310 q^{83} +(0.461838 - 17.3413i) q^{84} +(0.0131558 - 0.236978i) q^{85} +(2.14816 - 4.99689i) q^{86} +(10.0991 + 10.0991i) q^{87} +(9.72165 + 4.48963i) q^{88} +15.6390 q^{89} +(-3.53363 - 10.5244i) q^{90} +(-5.77276 + 5.77276i) q^{91} +(6.00475 + 0.159920i) q^{92} +4.21952i q^{93} +(-3.99914 + 1.59446i) q^{94} +(8.43775 + 0.468420i) q^{95} +(-6.39846 + 12.9384i) q^{96} +(5.00672 + 5.00672i) q^{97} +(2.54434 - 5.91846i) q^{98} +(-9.39839 + 9.39839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9}+O(q^{10}) $ 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9	$ 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} - 20 q^{15} - 6 q^{17} - 24 q^{18} - 2 q^{19} - 12 q^{20} - 16 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25} - 16 q^{26} - 24 q^{27} + 40 q^{28} + 14 q^{29} + 40 q^{30} + 20 q^{32} - 8 q^{33} + 28 q^{34} + 2 q^{35} - 4 q^{36} + 24 q^{38} + 44 q^{40} + 8 q^{42} - 44 q^{44} - 14 q^{45} + 12 q^{46} + 38 q^{47} + 4 q^{48} - 8 q^{50} + 8 q^{51} + 8 q^{52} + 12 q^{53} + 4 q^{54} - 6 q^{55} + 20 q^{56} - 24 q^{57} + 20 q^{58} + 10 q^{59} + 8 q^{60} + 14 q^{61} - 40 q^{62} - 6 q^{63} + 16 q^{64} + 4 q^{66} - 60 q^{68} - 32 q^{69} - 28 q^{70} + 24 q^{71} - 68 q^{72} - 14 q^{73} - 48 q^{74} + 16 q^{75} - 16 q^{76} - 44 q^{77} - 36 q^{78} - 16 q^{79} - 92 q^{80} + 2 q^{81} + 48 q^{82} + 40 q^{83} + 24 q^{84} + 14 q^{85} - 36 q^{86} + 24 q^{87} - 8 q^{88} + 12 q^{89} - 8 q^{90} - 8 q^{92} - 28 q^{94} + 34 q^{95} - 40 q^{96} + 18 q^{97} - 56 q^{98} + 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 - 20 * q^15 - 6 * q^17 - 24 * q^18 - 2 * q^19 - 12 * q^20 - 16 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 - 16 * q^26 - 24 * q^27 + 40 * q^28 + 14 * q^29 + 40 * q^30 + 20 * q^32 - 8 * q^33 + 28 * q^34 + 2 * q^35 - 4 * q^36 + 24 * q^38 + 44 * q^40 + 8 * q^42 - 44 * q^44 - 14 * q^45 + 12 * q^46 + 38 * q^47 + 4 * q^48 - 8 * q^50 + 8 * q^51 + 8 * q^52 + 12 * q^53 + 4 * q^54 - 6 * q^55 + 20 * q^56 - 24 * q^57 + 20 * q^58 + 10 * q^59 + 8 * q^60 + 14 * q^61 - 40 * q^62 - 6 * q^63 + 16 * q^64 + 4 * q^66 - 60 * q^68 - 32 * q^69 - 28 * q^70 + 24 * q^71 - 68 * q^72 - 14 * q^73 - 48 * q^74 + 16 * q^75 - 16 * q^76 - 44 * q^77 - 36 * q^78 - 16 * q^79 - 92 * q^80 + 2 * q^81 + 48 * q^82 + 40 * q^83 + 24 * q^84 + 14 * q^85 - 36 * q^86 + 24 * q^87 - 8 * q^88 + 12 * q^89 - 8 * q^90 - 8 * q^92 - 28 * q^94 + 34 * q^95 - 40 * q^96 + 18 * q^97 - 56 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.29924	−	0.558542i	−0.918703	−	0.394949i
$2$	−1.29924	−	0.558542i	−0.918703	−	0.394949i
$3$	−2.55161			−1.47317			−0.736586	−	0.676344i	$-0.763563\pi$
$3$	−2.55161			−1.47317			−0.736586	+	0.676344i	$0.763563\pi$
$4$	1.37606	+	1.45136i	0.688031	+	0.725681i
$5$	1.49107	+	1.66635i	0.666825	+	0.745214i
$5$	1.49107	+	1.66635i	0.666825	+	0.745214i
$6$	3.31516	+	1.42518i	1.35341	+	0.581827i
$7$	2.40368	+	2.40368i	0.908504	+	0.908504i	0.996152	−	0.0876474i	$-0.0279349\pi$
$7$	2.40368	+	2.40368i	0.908504	+	0.908504i	−0.0876474	+	0.996152i	$0.527935\pi$
$8$	−0.977191	−	2.65426i	−0.345489	−	0.938423i
$9$	3.51070			1.17023
$10$	−1.00653	−	2.99782i	−0.318293	−	0.947992i
$11$	−2.67707	+	2.67707i	−0.807167	+	0.807167i	−0.984204	−	0.177037i	$-0.943349\pi$
$11$	−2.67707	+	2.67707i	−0.807167	+	0.807167i	0.177037	+	0.984204i	$0.443349\pi$
$12$	−3.51117	−	3.70331i	−1.01359	−	1.06905i
$13$			2.40164i			0.666094i	0.942910	+	0.333047i	$0.108077\pi$
$13$			2.40164i			0.666094i	−0.942910	+	0.333047i	$0.891923\pi$
$14$	−1.78040	−	4.46551i	−0.475833	−	1.19346i
$15$	−3.80462	−	4.25187i	−0.982348	−	1.09783i
$16$	−0.212908	+	3.99433i	−0.0532269	+	0.998582i
$17$	−0.0750544	−	0.0750544i	−0.0182034	−	0.0182034i	0.697947	−	0.716150i	$-0.254097\pi$
$17$	−0.0750544	−	0.0750544i	−0.0182034	−	0.0182034i	−0.716150	+	0.697947i	$0.754097\pi$
$18$	−4.56125	−	1.96087i	−1.07510	−	0.462182i
$19$	2.67236	−	2.67236i	0.613081	−	0.613081i	−0.330666	−	0.943748i	$-0.607274\pi$
$19$	2.67236	−	2.67236i	0.613081	−	0.613081i	0.943748	+	0.330666i	$0.107274\pi$
$20$	−0.366678	+	4.45708i	−0.0819918	+	0.996633i
$21$	−6.13324	−	6.13324i	−1.33838	−	1.33838i
$22$	4.97342	−	1.98291i	1.06034	−	0.422757i
$23$	2.12375	−	2.12375i	0.442833	−	0.442833i	−0.450130	−	0.892963i	$-0.648622\pi$
$23$	2.12375	−	2.12375i	0.442833	−	0.442833i	0.892963	+	0.450130i	$0.148622\pi$
$24$	2.49341	+	6.77263i	0.508965	+	1.38246i
$25$	−0.553442	+	4.96928i	−0.110688	+	0.993855i
$26$	1.34141	−	3.12031i	0.263073	−	0.611943i
$27$	−1.30310			−0.250783
$28$	−0.180999	+	6.79621i	−0.0342056	+	1.28436i
$29$	−3.95795	−	3.95795i	−0.734974	−	0.734974i	0.236627	−	0.971601i	$-0.423958\pi$
$29$	−3.95795	−	3.95795i	−0.734974	−	0.734974i	−0.971601	+	0.236627i	$0.923958\pi$
$30$	2.56827	+	7.64925i	0.468900	+	1.39656i
$31$		−	1.65367i		−	0.297008i	−0.988912	−	0.148504i	$-0.952554\pi$
$31$		−	1.65367i		−	0.297008i	0.988912	−	0.148504i	$-0.0474458\pi$
$32$	2.50762	−	5.07068i	0.443289	−	0.896379i
$33$	6.83083	−	6.83083i	1.18909	−	1.18909i
$34$	0.0555929	+	0.139435i	0.00953410	+	0.0239129i
$35$	−0.421324	+	7.58941i	−0.0712168	+	1.28284i
$36$	4.83094	+	5.09530i	0.805157	+	0.849216i
$37$		−	2.53082i		−	0.416064i	−0.978122	−	0.208032i	$-0.933294\pi$
$37$		−	2.53082i		−	0.416064i	0.978122	−	0.208032i	$-0.0667059\pi$
$38$	−4.96467	+	1.97942i	−0.805375	+	0.321104i
$39$		−	6.12803i		−	0.981271i
$40$	2.96587	−	5.58602i	0.468945	−	0.883227i
$41$			1.70882i			0.266873i	0.991057	+	0.133436i	$0.0426012\pi$
$41$			1.70882i			0.266873i	−0.991057	+	0.133436i	$0.957399\pi$
$42$	4.54289	+	11.3942i	0.700983	+	1.75817i
$43$			3.84601i			0.586510i	0.956034	+	0.293255i	$0.0947386\pi$
$43$			3.84601i			0.586510i	−0.956034	+	0.293255i	$0.905261\pi$
$44$	−7.56921	−	0.201586i	−1.14110	−	0.0303902i
$45$	5.23469	+	5.85005i	0.780341	+	0.872074i
$46$	−3.94547	+	1.57306i	−0.581728	+	0.231936i
$47$	2.15264	−	2.15264i	0.313995	−	0.313995i	−0.532460	−	0.846455i	$-0.678732\pi$
$47$	2.15264	−	2.15264i	0.313995	−	0.313995i	0.846455	+	0.532460i	$0.178732\pi$
$48$	0.543256	−	10.1920i	0.0784123	−	1.47108i
$49$			4.55532i			0.650760i
$50$	3.49460	−	6.14717i	0.494212	−	0.869342i
$51$	0.191509	+	0.191509i	0.0268167	+	0.0268167i
$52$	−3.48565	+	3.30480i	−0.483372	+	0.458293i
$53$	−1.29475			−0.177848			−0.0889239	−	0.996038i	$-0.528343\pi$
$53$	−1.29475			−0.177848			−0.0889239	+	0.996038i	$0.528343\pi$
$54$	1.69305	+	0.727839i	0.230395	+	0.0990463i
$55$	−8.45262	−	0.469246i	−1.13975	−	0.0632731i
$56$	4.03113	−	8.72883i	0.538683	−	1.16644i
$57$	−6.81881	+	6.81881i	−0.903174	+	0.903174i
$58$	2.93166	+	7.35302i	0.384946	+	0.965499i
$59$	5.29614	+	5.29614i	0.689499	+	0.689499i	0.962121	−	0.272622i	$-0.0878908\pi$
$59$	5.29614	+	5.29614i	0.689499	+	0.689499i	−0.272622	+	0.962121i	$0.587891\pi$
$60$	0.935619	−	11.3727i	0.120788	−	1.46821i
$61$	10.2413	−	10.2413i	1.31126	−	1.31126i	0.390780	−	0.920484i	$-0.372205\pi$
$61$	10.2413	−	10.2413i	1.31126	−	1.31126i	0.920484	−	0.390780i	$-0.127795\pi$
$62$	−0.923645	+	2.14852i	−0.117303	+	0.272862i
$63$	8.43858	+	8.43858i	1.06316	+	1.06316i
$64$	−6.09020	+	5.18744i	−0.761274	+	0.648430i
$65$	−4.00197	+	3.58100i	−0.496383	+	0.444168i
$66$	−12.6902	+	5.05960i	−1.56206	+	0.622794i
$67$		−	10.6230i		−	1.29780i	−0.760873	−	0.648901i	$-0.775229\pi$
$67$		−	10.6230i		−	1.29780i	0.760873	−	0.648901i	$-0.224771\pi$
$68$	0.00565167	−	0.212211i	0.000685365	−	0.0257343i
$69$	−5.41898	+	5.41898i	−0.652369	+	0.652369i
$70$	4.78640	−	9.62515i	0.572085	−	1.15043i
$71$	2.27322			0.269781			0.134891	−	0.990860i	$-0.456932\pi$
$71$	2.27322			0.269781			0.134891	+	0.990860i	$0.456932\pi$
$72$	−3.43062	−	9.31831i	−0.404303	−	1.09817i
$73$	−9.99096	−	9.99096i	−1.16935	−	1.16935i	−0.982361	−	0.186992i	$-0.940126\pi$
$73$	−9.99096	−	9.99096i	−1.16935	−	1.16935i	−0.186992	−	0.982361i	$-0.559874\pi$
$74$	−1.41357	+	3.28815i	−0.164324	+	0.382240i
$75$	1.41217	−	12.6796i	0.163063	−	1.46412i
$76$	7.55589	+	0.201231i	0.866720	+	0.0230828i
$77$	−12.8696			−1.46663
$78$	−3.42276	+	7.96180i	−0.387552	+	0.901496i
$79$	−8.70617			−0.979520			−0.489760	−	0.871857i	$-0.662916\pi$
$79$	−8.70617			−0.979520			−0.489760	+	0.871857i	$0.662916\pi$
$80$	−6.97341	+	5.60103i	−0.779651	+	0.626214i
$81$	−7.20709			−0.800787
$82$	0.954448	−	2.22017i	0.105401	−	0.245177i
$83$	11.1310			1.22178			0.610890	−	0.791715i	$-0.290812\pi$
$83$	11.1310			1.22178			0.610890	+	0.791715i	$0.290812\pi$
$84$	0.461838	−	17.3413i	0.0503907	−	1.89209i
$85$	0.0131558	−	0.236978i	0.00142695	−	0.0257039i
$86$	2.14816	−	4.99689i	0.231642	−	0.538829i
$87$	10.0991	+	10.0991i	1.08274	+	1.08274i
$88$	9.72165	+	4.48963i	1.03633	+	0.478596i
$89$	15.6390			1.65773			0.828866	−	0.559447i	$-0.188986\pi$
$89$	15.6390			1.65773			0.828866	+	0.559447i	$0.188986\pi$
$90$	−3.53363	−	10.5244i	−0.372477	−	1.10937i
$91$	−5.77276	+	5.77276i	−0.605149	+	0.605149i
$92$	6.00475	+	0.159920i	0.626038	+	0.0166729i
$93$			4.21952i			0.437544i
$94$	−3.99914	+	1.59446i	−0.412480	+	0.164456i
$95$	8.43775	+	0.468420i	0.865695	+	0.0480589i
$96$	−6.39846	+	12.9384i	−0.653040	+	1.32052i
$97$	5.00672	+	5.00672i	0.508355	+	0.508355i	0.914021	−	0.405666i	$-0.132960\pi$
$97$	5.00672	+	5.00672i	0.508355	+	0.508355i	−0.405666	+	0.914021i	$0.632960\pi$
$98$	2.54434	−	5.91846i	0.257017	−	0.597855i
$99$	−9.39839	+	9.39839i	−0.944573	+	0.944573i
$100$	−7.97379	+	6.03478i	−0.797379	+	0.603478i
$101$	6.37101	+	6.37101i	0.633939	+	0.633939i	0.949054	−	0.315115i	$-0.102043\pi$
$101$	6.37101	+	6.37101i	0.633939	+	0.633939i	−0.315115	+	0.949054i	$0.602043\pi$
$102$	−0.141851	−	0.355783i	−0.0140454	−	0.0352278i
$103$	−1.93695	+	1.93695i	−0.190854	+	0.190854i	−0.796065	−	0.605211i	$-0.793089\pi$
$103$	−1.93695	+	1.93695i	−0.190854	+	0.190854i	0.605211	+	0.796065i	$0.293089\pi$
$104$	6.37457	−	2.34686i	0.625078	−	0.230128i
$105$	1.07505	−	19.3652i	0.104915	−	1.88985i
$106$	1.68220	+	0.723173i	0.163389	+	0.0702408i
$107$	6.97778			0.674568			0.337284	−	0.941403i	$-0.390492\pi$
$107$	6.97778			0.674568			0.337284	+	0.941403i	$0.390492\pi$
$108$	−1.79315	−	1.89128i	−0.172546	−	0.181988i
$109$	0.277748	+	0.277748i	0.0266034	+	0.0266034i	0.720283	−	0.693680i	$-0.244012\pi$
$109$	0.277748	+	0.277748i	0.0266034	+	0.0266034i	−0.693680	+	0.720283i	$0.744012\pi$
$110$	10.7199	+	5.33081i	1.02210	+	0.508273i
$111$			6.45766i			0.612934i
$112$	−10.1128	+	9.08931i	−0.955573	+	0.858859i
$113$	−8.75577	+	8.75577i	−0.823674	+	0.823674i	−0.986633	−	0.162959i	$-0.947896\pi$
$113$	−8.75577	+	8.75577i	−0.823674	+	0.823674i	0.162959	+	0.986633i	$0.447896\pi$
$114$	12.6679	−	5.05070i	1.18646	−	0.473041i
$115$	6.70557	+	0.372258i	0.625298	+	0.0347133i
$116$	0.298037	−	11.1908i	0.0276721	−	1.03904i
$117$			8.43142i			0.779485i
$118$	−3.92286	−	9.83909i	−0.361128	−	0.905762i
$119$		−	0.360813i		−	0.0330757i
$120$	−7.56773	+	14.2533i	−0.690836	+	1.30114i
$121$		−	3.33340i		−	0.303036i
$122$	−19.0261	+	7.58574i	−1.72254	+	0.686780i
$123$		−	4.36024i		−	0.393149i
$124$	2.40008	−	2.27555i	0.215533	−	0.204351i
$125$	−9.10577	+	6.48729i	−0.814445	+	0.580241i
$126$	−6.25046	−	15.6771i	−0.556836	−	1.39662i
$127$	−0.679502	+	0.679502i	−0.0602961	+	0.0602961i	−0.736612	−	0.676316i	$-0.763576\pi$
$127$	−0.679502	+	0.679502i	−0.0602961	+	0.0602961i	0.676316	+	0.736612i	$0.263576\pi$
$128$	10.8100	−	3.33811i	0.955482	−	0.295050i
$129$		−	9.81350i		−	0.864030i
$130$	7.19966	−	2.41732i	0.631452	−	0.212013i
$131$	−5.43859	−	5.43859i	−0.475172	−	0.475172i	0.428412	−	0.903584i	$-0.359073\pi$
$131$	−5.43859	−	5.43859i	−0.475172	−	0.475172i	−0.903584	+	0.428412i	$0.859073\pi$
$132$	19.3137	+	0.514367i	1.68104	+	0.0447699i
$133$	12.8470			1.11397
$134$	−5.93337	+	13.8018i	−0.512565	+	1.19229i
$135$	−1.94302	−	2.17143i	−0.167228	−	0.186887i
$136$	−0.125871	+	0.272557i	−0.0107934	+	0.0233715i
$137$	−7.47496	+	7.47496i	−0.638629	+	0.638629i	−0.950217	−	0.311588i	$-0.899139\pi$
$137$	−7.47496	+	7.47496i	−0.638629	+	0.638629i	0.311588	+	0.950217i	$0.399139\pi$
$138$	10.0673	−	4.01384i	0.856986	−	0.341681i
$139$	−11.5307	−	11.5307i	−0.978023	−	0.978023i	0.0217404	−	0.999764i	$-0.493079\pi$
$139$	−11.5307	−	11.5307i	−0.978023	−	0.978023i	−0.999764	+	0.0217404i	$0.993079\pi$
$140$	−11.5947	+	9.83200i	−0.979935	+	0.830955i
$141$	−5.49270	+	5.49270i	−0.462568	+	0.462568i
$142$	−2.95346	−	1.26969i	−0.247849	−	0.106550i
$143$	−6.42935	−	6.42935i	−0.537649	−	0.537649i
$144$	−0.747455	+	14.0229i	−0.0622879	+	1.16857i
$145$	0.693763	−	12.4969i	0.0576139	−	1.03781i
$146$	7.40031	+	18.5611i	0.612454	+	1.53612i
$147$		−	11.6234i		−	0.958680i
$148$	3.67314	−	3.48257i	0.301930	−	0.286265i
$149$	5.51174	−	5.51174i	0.451539	−	0.451539i	−0.444326	−	0.895865i	$-0.646557\pi$
$149$	5.51174	−	5.51174i	0.451539	−	0.451539i	0.895865	+	0.444326i	$0.146557\pi$
$150$	−8.91686	+	15.6852i	−0.728058	+	1.28069i
$151$	−4.13617			−0.336597			−0.168299	−	0.985736i	$-0.553827\pi$
$151$	−4.13617			−0.336597			−0.168299	+	0.985736i	$0.553827\pi$
$152$	−9.70454	−	4.48173i	−0.787142	−	0.363516i
$153$	−0.263494	−	0.263494i	−0.0213022	−	0.0213022i
$154$	16.7207	+	7.18822i	1.34740	+	0.579243i
$155$	2.75559	−	2.46573i	0.221335	−	0.198052i
$156$	8.89400	−	8.43255i	0.712090	−	0.675144i
$157$	20.2700			1.61772			0.808861	−	0.587999i	$-0.200084\pi$
$157$	20.2700			1.61772			0.808861	+	0.587999i	$0.200084\pi$
$158$	11.3114	+	4.86276i	0.899889	+	0.386860i
$159$	3.30370			0.262000
$160$	12.1886	−	3.38216i	0.963590	−	0.267383i
$161$	10.2096			0.804631
$162$	9.36375	+	4.02546i	0.735686	+	0.316270i
$163$	−13.1835			−1.03262			−0.516308	−	0.856403i	$-0.672694\pi$
$163$	−13.1835			−1.03262			−0.516308	+	0.856403i	$0.672694\pi$
$164$	−2.48012	+	2.35144i	−0.193665	+	0.183617i
$165$	21.5678	+	1.19733i	1.67905	+	0.0932121i
$166$	−14.4618	−	6.21710i	−1.12245	−	0.482541i
$167$	−11.8190	−	11.8190i	−0.914585	−	0.914585i	0.0820441	−	0.996629i	$-0.473855\pi$
$167$	−11.8190	−	11.8190i	−0.914585	−	0.914585i	−0.996629	+	0.0820441i	$0.973855\pi$
$168$	−10.2859	+	22.2726i	−0.793572	+	1.71836i
$169$	7.23214			0.556319
$170$	−0.149455	+	0.300544i	−0.0114627	+	0.0230507i
$171$	9.38185	−	9.38185i	0.717448	−	0.717448i
$172$	−5.58195	+	5.29234i	−0.425620	+	0.403537i
$173$		−	15.5763i		−	1.18424i	−0.805849	−	0.592120i	$-0.798291\pi$
$173$		−	15.5763i		−	1.18424i	0.805849	−	0.592120i	$-0.201709\pi$
$174$	−7.48044	−	18.7620i	−0.567091	−	1.42235i
$175$	−13.2748	+	10.6142i	−1.00348	+	0.802361i
$176$	−10.1231	−	11.2631i	−0.763060	−	0.848986i
$177$	−13.5137	−	13.5137i	−1.01575	−	1.01575i
$178$	−20.3189	−	8.73505i	−1.52296	−	0.654719i
$179$	−15.5963	+	15.5963i	−1.16572	+	1.16572i	−0.182523	+	0.983202i	$0.558426\pi$
$179$	−15.5963	+	15.5963i	−1.16572	+	1.16572i	−0.983202	+	0.182523i	$0.941574\pi$
$180$	−1.28730	+	15.6475i	−0.0959495	+	1.16629i
$181$	2.98705	+	2.98705i	0.222026	+	0.222026i	0.809351	−	0.587325i	$-0.199819\pi$
$181$	2.98705	+	2.98705i	0.222026	+	0.222026i	−0.587325	+	0.809351i	$0.699819\pi$
$182$	10.7245	−	4.27588i	0.794955	−	0.316950i
$183$	−26.1318	+	26.1318i	−1.93172	+	1.93172i
$184$	−7.71230	−	3.56168i	−0.568559	−	0.262571i
$185$	4.21723	−	3.77362i	0.310057	−	0.277442i
$186$	2.35678	−	5.48218i	0.172807	−	0.401973i
$187$	0.401852			0.0293863
$188$	6.08643	+	0.162096i	0.443899	+	0.0118221i
$189$	−3.13224	−	3.13224i	−0.227837	−	0.227837i
$190$	−10.7010	−	5.32143i	−0.776336	−	0.386057i
$191$			6.47168i			0.468274i	0.972204	+	0.234137i	$0.0752264\pi$
$191$			6.47168i			0.468274i	−0.972204	+	0.234137i	$0.924774\pi$
$192$	15.5398	−	13.2363i	1.12149	−	0.955248i
$193$	−11.1131	+	11.1131i	−0.799936	+	0.799936i	−0.983085	−	0.183149i	$-0.941371\pi$
$193$	−11.1131	+	11.1131i	−0.799936	+	0.799936i	0.183149	+	0.983085i	$0.441371\pi$
$194$	−3.70848	−	9.30141i	−0.266253	−	0.667802i
$195$	10.2114	−	9.13730i	0.731257	−	0.654336i
$196$	−6.61142	+	6.26840i	−0.472244	+	0.447743i
$197$		−	25.0927i		−	1.78778i	−0.448288	−	0.893889i	$-0.647966\pi$
$197$		−	25.0927i		−	1.78778i	0.448288	−	0.893889i	$-0.352034\pi$
$198$	17.4602	−	6.96139i	1.24084	−	0.494724i
$199$		−	18.7579i		−	1.32972i	−0.746970	−	0.664858i	$-0.768492\pi$
$199$		−	18.7579i		−	1.32972i	0.746970	−	0.664858i	$-0.231508\pi$
$200$	13.7306	−	3.38695i	0.970898	−	0.239494i
$201$			27.1056i			1.91188i
$202$	−4.71901	−	11.8360i	−0.332028	−	0.832775i
$203$		−	19.0273i		−	1.33545i
$204$	−0.0144208	+	0.541479i	−0.00100966	+	0.0379111i
$205$	−2.84749	+	2.54796i	−0.198877	+	0.177958i
$206$	3.59844	−	1.43470i	0.250715	−	0.0999604i
$207$	7.45586	−	7.45586i	0.518218	−	0.518218i
$208$	−9.59293	−	0.511327i	−0.665150	−	0.0354541i
$209$			14.3082i			0.989718i
$210$	−12.2130	+	24.5596i	−0.842779	+	1.69477i
$211$	6.38863	+	6.38863i	0.439811	+	0.439811i	0.891948	−	0.452137i	$-0.149338\pi$
$211$	6.38863	+	6.38863i	0.439811	+	0.439811i	−0.452137	+	0.891948i	$0.649338\pi$
$212$	−1.78166	−	1.87915i	−0.122365	−	0.129061i
$213$	−5.80036			−0.397434
$214$	−9.06583	−	3.89738i	−0.619727	−	0.266420i
$215$	−6.40879	+	5.73465i	−0.437076	+	0.391100i
$216$	1.27338	+	3.45878i	0.0866427	+	0.235340i
$217$	3.97489	−	3.97489i	0.269833	−	0.269833i
$218$	−0.205728	−	0.515996i	−0.0139337	−	0.0349476i
$219$	25.4930	+	25.4930i	1.72266	+	1.72266i
$220$	−10.9503	−	12.9135i	−0.738268	−	0.870630i
$221$	0.180253	−	0.180253i	0.0121252	−	0.0121252i
$222$	3.60687	−	8.39006i	0.242077	−	0.563104i
$223$	−4.29779	−	4.29779i	−0.287801	−	0.287801i	0.548409	−	0.836210i	$-0.315234\pi$
$223$	−4.29779	−	4.29779i	−0.287801	−	0.287801i	−0.836210	+	0.548409i	$0.815234\pi$
$224$	18.2158	−	6.16078i	1.21709	−	0.411634i
$225$	−1.94297	+	17.4456i	−0.129531	+	1.16304i
$226$	16.2663	−	6.48541i	1.08202	−	0.431403i
$227$			29.1029i			1.93163i	0.259241	+	0.965813i	$0.416528\pi$
$227$			29.1029i			1.93163i	−0.259241	+	0.965813i	$0.583472\pi$
$228$	−19.2797	−	0.513462i	−1.27683	−	0.0340049i
$229$	−18.3405	+	18.3405i	−1.21198	+	1.21198i	−0.241600	+	0.970376i	$0.577672\pi$
$229$	−18.3405	+	18.3405i	−1.21198	+	1.21198i	−0.970376	+	0.241600i	$0.922328\pi$
$230$	−8.50424	−	4.22900i	−0.560753	−	0.278852i
$231$	32.8382			2.16060
$232$	−6.63776	+	14.3731i	−0.435790	+	0.943641i
$233$	1.46663	+	1.46663i	0.0960824	+	0.0960824i	0.753514	−	0.657432i	$-0.228357\pi$
$233$	1.46663	+	1.46663i	0.0960824	+	0.0960824i	−0.657432	+	0.753514i	$0.728357\pi$
$234$	4.70930	−	10.9545i	0.307857	−	0.716116i
$235$	6.79678	+	0.377322i	0.443373	+	0.0246138i
$236$	−0.398804	+	14.9744i	−0.0259600	+	0.974754i
$237$	22.2147			1.44300
$238$	−0.201529	+	0.468784i	−0.0130632	+	0.0303867i
$239$	12.5432			0.811352			0.405676	−	0.914017i	$-0.367036\pi$
$239$	12.5432			0.811352			0.405676	+	0.914017i	$0.367036\pi$
$240$	17.7934	−	14.2916i	1.14856	−	0.922521i
$241$	14.8870			0.958954			0.479477	−	0.877554i	$-0.340826\pi$
$241$	14.8870			0.958954			0.479477	+	0.877554i	$0.340826\pi$
$242$	−1.86184	+	4.33089i	−0.119684	+	0.278400i
$243$	22.2990			1.43048
$244$	28.9565	+	0.771179i	1.85375	+	0.0493697i
$245$	−7.59075	+	6.79228i	−0.484955	+	0.433943i
$246$	−2.43538	+	5.66501i	−0.155274	+	0.361188i
$247$	6.41803	+	6.41803i	0.408370	+	0.408370i
$248$	−4.38927	+	1.61595i	−0.278719	+	0.102613i
$249$	−28.4018			−1.79989
$250$	15.4540	−	3.34261i	0.977399	−	0.211405i
$251$	−5.38459	+	5.38459i	−0.339872	+	0.339872i	−0.856319	−	0.516447i	$-0.827254\pi$
$251$	−5.38459	+	5.38459i	−0.339872	+	0.339872i	0.516447	+	0.856319i	$0.327254\pi$
$252$	−0.635433	+	23.8595i	−0.0400285	+	1.50300i
$253$			11.3709i			0.714880i
$254$	1.26237	−	0.503308i	0.0792081	−	0.0315803i
$255$	−0.0335684	+	0.604675i	−0.00210214	+	0.0378662i
$256$	−15.9093	−	1.70085i	−0.994334	−	0.106303i
$257$	−3.88657	−	3.88657i	−0.242437	−	0.242437i	0.575420	−	0.817858i	$-0.304838\pi$
$257$	−3.88657	−	3.88657i	−0.242437	−	0.242437i	−0.817858	+	0.575420i	$0.804838\pi$
$258$	−5.48125	+	12.7501i	−0.341248	+	0.793787i
$259$	6.08327	−	6.08327i	0.377996	−	0.377996i
$260$	−10.7043	−	0.880628i	−0.663851	−	0.0546142i
$261$	−13.8952	−	13.8952i	−0.860090	−	0.860090i
$262$	4.02836	+	10.1037i	0.248873	+	0.624210i
$263$	16.9658	−	16.9658i	1.04615	−	1.04615i	0.0472716	−	0.998882i	$-0.484947\pi$
$263$	16.9658	−	16.9658i	1.04615	−	1.04615i	0.998882	−	0.0472716i	$-0.0150526\pi$
$264$	−24.8058	−	11.4558i	−1.52669	−	0.705054i
$265$	−1.93056	−	2.15751i	−0.118593	−	0.132535i
$266$	−16.6913	−	7.17557i	−1.02341	−	0.439963i
$267$	−39.9046			−2.44212
$268$	15.4178	−	14.6179i	0.941791	−	0.892928i
$269$	2.55482	+	2.55482i	0.155770	+	0.155770i	0.780689	−	0.624919i	$-0.214868\pi$
$269$	2.55482	+	2.55482i	0.155770	+	0.155770i	−0.624919	+	0.780689i	$0.714868\pi$
$270$	1.31161	+	3.90647i	0.0798223	+	0.237740i
$271$		−	3.33684i		−	0.202698i	−0.994851	−	0.101349i	$-0.967684\pi$
$271$		−	3.33684i		−	0.202698i	0.994851	−	0.101349i	$-0.0323159\pi$
$272$	0.315772	−	0.283813i	0.0191465	−	0.0172087i
$273$	14.7298	−	14.7298i	0.891488	−	0.891488i
$274$	13.8869	−	5.53671i	0.838937	−	0.334485i
$275$	−11.8215	−	14.7847i	−0.712863	−	0.891551i
$276$	−15.3218	−	0.408054i	−0.922262	−	0.0245620i
$277$			4.60736i			0.276830i	0.990374	+	0.138415i	$0.0442007\pi$
$277$			4.60736i			0.276830i	−0.990374	+	0.138415i	$0.955799\pi$
$278$	8.54081	+	21.4216i	0.512244	+	1.28478i
$279$		−	5.80554i		−	0.347569i
$280$	20.5560	−	6.29799i	1.22845	−	0.376377i
$281$		−	22.1178i		−	1.31944i	−0.751513	−	0.659718i	$-0.770676\pi$
$281$		−	22.1178i		−	1.31944i	0.751513	−	0.659718i	$-0.229324\pi$
$282$	10.2042	−	4.06844i	0.607654	−	0.242272i
$283$			10.8629i			0.645734i	0.946444	+	0.322867i	$0.104647\pi$
$283$			10.8629i			0.645734i	−0.946444	+	0.322867i	$0.895353\pi$
$284$	3.12809	+	3.29926i	0.185618	+	0.195775i
$285$	−21.5298	−	1.19522i	−1.27532	−	0.0707990i
$286$	4.76222	+	11.9443i	0.281596	+	0.706284i
$287$	−4.10745	+	4.10745i	−0.242455	+	0.242455i
$288$	8.80350	−	17.8017i	0.518751	−	1.04897i
$289$		−	16.9887i		−	0.999337i
$290$	−7.88141	+	15.8490i	−0.462813	+	0.930686i
$291$	−12.7752	−	12.7752i	−0.748895	−	0.748895i
$292$	0.752328	−	28.2487i	0.0440267	−	1.65313i
$293$	−18.4067			−1.07533			−0.537665	−	0.843159i	$-0.680693\pi$
$293$	−18.4067			−1.07533			−0.537665	+	0.843159i	$0.680693\pi$
$294$	−6.49214	+	15.1016i	−0.378630	+	0.880743i
$295$	−0.928326	+	16.7221i	−0.0540492	+	0.973600i
$296$	−6.71746	+	2.47309i	−0.390444	+	0.143746i
$297$	3.48850	−	3.48850i	0.202423	−	0.202423i
$298$	−10.2396	+	4.08255i	−0.593166	+	0.236496i
$299$	5.10048	+	5.10048i	0.294968	+	0.294968i
$300$	20.3460	−	15.3984i	1.17468	−	0.889027i
$301$	−9.24455	+	9.24455i	−0.532847	+	0.532847i
$302$	5.37389	+	2.31023i	0.309233	+	0.132939i
$303$	−16.2563	−	16.2563i	−0.933900	−	0.933900i
$304$	10.1053	+	11.2432i	0.579580	+	0.644845i
$305$	32.3360	+	1.79513i	1.85156	+	0.102789i
$306$	0.195170	+	0.489514i	0.0111571	+	0.0279837i
$307$		−	6.60872i		−	0.377180i	−0.982056	−	0.188590i	$-0.939608\pi$
$307$		−	6.60872i		−	0.377180i	0.982056	−	0.188590i	$-0.0603917\pi$
$308$	−17.7094	−	18.6785i	−1.00909	−	1.06431i
$309$	4.94234	−	4.94234i	0.281160	−	0.281160i
$310$	−4.95740	+	1.66447i	−0.281561	+	0.0945356i
$311$	−0.606102			−0.0343689			−0.0171845	−	0.999852i	$-0.505470\pi$
$311$	−0.606102			−0.0343689			−0.0171845	+	0.999852i	$0.505470\pi$
$312$	−16.2654	+	5.98826i	−0.920847	+	0.339018i
$313$	19.3708	+	19.3708i	1.09490	+	1.09490i	0.994997	+	0.0999032i	$0.0318533\pi$
$313$	19.3708	+	19.3708i	1.09490	+	1.09490i	0.0999032	+	0.994997i	$0.468147\pi$
$314$	−26.3357	−	11.3216i	−1.48621	−	0.638918i
$315$	−1.47914	+	26.6441i	−0.0833403	+	1.50123i
$316$	−11.9802	−	12.6358i	−0.673940	−	0.710820i
$317$	−7.04328			−0.395590			−0.197795	−	0.980243i	$-0.563378\pi$
$317$	−7.04328			−0.395590			−0.197795	+	0.980243i	$0.563378\pi$
$318$	−4.29230	−	1.84525i	−0.240700	−	0.103477i
$319$	21.1914			1.18649
$320$	−17.7250	−	2.41358i	−0.990856	−	0.134923i
$321$	−17.8046			−0.993753
$322$	−13.2648	−	5.70250i	−0.739217	−	0.317788i
$323$	−0.401145			−0.0223203
$324$	−9.91740	−	10.4601i	−0.550967	−	0.581117i
$325$	−11.9344	−	1.32917i	−0.662001	−	0.0737290i
$326$	17.1286	+	7.36356i	0.948667	+	0.407830i
$327$	−0.708703	−	0.708703i	−0.0391914	−	0.0391914i
$328$	4.53565	−	1.66984i	0.250440	−	0.0922017i
$329$	10.3485			0.570532
$330$	−27.3530	−	13.6021i	−1.50573	−	0.748772i
$331$	−13.2275	+	13.2275i	−0.727047	+	0.727047i	−0.970031	−	0.242983i	$-0.921874\pi$
$331$	−13.2275	+	13.2275i	−0.727047	+	0.727047i	0.242983	+	0.970031i	$0.421874\pi$
$332$	15.3169	+	16.1550i	0.840623	+	0.886624i
$333$		−	8.88495i		−	0.486892i
$334$	8.75437	+	21.9572i	0.479018	+	1.20145i
$335$	17.7016	−	15.8395i	0.967140	−	0.865407i
$336$	25.8040	−	23.1924i	1.40772	−	1.26525i
$337$	7.73287	+	7.73287i	0.421236	+	0.421236i	0.885629	−	0.464393i	$-0.153727\pi$
$337$	7.73287	+	7.73287i	0.421236	+	0.421236i	−0.464393	+	0.885629i	$0.653727\pi$
$338$	−9.39631	−	4.03945i	−0.511092	−	0.219717i
$339$	22.3413	−	22.3413i	1.21341	−	1.21341i
$340$	0.362044	−	0.307003i	0.0196346	−	0.0166496i
$341$	4.42699	+	4.42699i	0.239735	+	0.239735i
$342$	−17.4295	+	6.94914i	−0.942477	+	0.375767i
$343$	5.87623	−	5.87623i	0.317286	−	0.317286i
$344$	10.2083	−	3.75828i	0.550395	−	0.202633i
$345$	−17.1100	−	0.949857i	−0.921170	−	0.0511386i
$346$	−8.69999	+	20.2373i	−0.467714	+	1.08797i
$347$	−11.3945			−0.611691			−0.305845	−	0.952081i	$-0.598939\pi$
$347$	−11.3945			−0.611691			−0.305845	+	0.952081i	$0.598939\pi$
$348$	−0.760474	+	28.5546i	−0.0407657	+	1.53069i
$349$	−12.0508	−	12.0508i	−0.645066	−	0.645066i	0.306730	−	0.951796i	$-0.400765\pi$
$349$	−12.0508	−	12.0508i	−0.645066	−	0.645066i	−0.951796	+	0.306730i	$0.900765\pi$
$350$	23.1757	−	6.37591i	1.23879	−	0.340807i
$351$		−	3.12958i		−	0.167045i
$352$	6.86150	+	20.2876i	0.365719	+	1.08134i
$353$	−6.47876	+	6.47876i	−0.344830	+	0.344830i	−0.858179	−	0.513350i	$-0.828404\pi$
$353$	−6.47876	+	6.47876i	−0.344830	+	0.344830i	0.513350	+	0.858179i	$0.328404\pi$
$354$	10.0096	+	25.1055i	0.532004	+	1.33434i
$355$	3.38952	+	3.78798i	0.179897	+	0.201045i
$356$	21.5203	+	22.6979i	1.14057	+	1.20299i
$357$			0.920653i			0.0487261i
$358$	28.9746	−	11.5522i	1.53136	−	0.610553i
$359$		−	3.25098i		−	0.171580i	−0.996313	−	0.0857902i	$-0.972659\pi$
$359$		−	3.25098i		−	0.171580i	0.996313	−	0.0857902i	$-0.0273415\pi$
$360$	10.4123	−	19.6108i	0.548775	−	1.03358i
$361$			4.71699i			0.248263i
$362$	−2.21251	−	5.54929i	−0.116287	−	0.291664i
$363$			8.50553i			0.446424i
$364$	−16.3220	−	0.434694i	−0.855507	−	0.0227841i
$365$	1.75125	−	31.5456i	0.0916646	−	1.65117i
$366$	48.5472	−	19.3558i	2.53760	−	1.01174i
$367$	−12.7038	+	12.7038i	−0.663132	+	0.663132i	−0.956117	−	0.292985i	$-0.905351\pi$
$367$	−12.7038	+	12.7038i	−0.663132	+	0.663132i	0.292985	+	0.956117i	$0.405351\pi$
$368$	8.03080	+	8.93513i	0.418635	+	0.465776i
$369$			5.99916i			0.312304i
$370$	−7.58693	+	2.54735i	−0.394426	+	0.132430i
$371$	−3.11216	−	3.11216i	−0.161575	−	0.161575i
$372$	−6.12405	+	5.80632i	−0.317517	+	0.301044i
$373$	21.9761			1.13788			0.568939	−	0.822379i	$-0.307354\pi$
$373$	21.9761			1.13788			0.568939	+	0.822379i	$0.307354\pi$
$374$	−0.522103	−	0.224451i	−0.0269973	−	0.0116061i
$375$	23.2343	−	16.5530i	1.19982	−	0.854794i
$376$	−7.81721	−	3.61013i	−0.403142	−	0.186178i
$377$	9.50557	−	9.50557i	0.489562	−	0.489562i
$378$	2.32005	+	5.81903i	0.119331	+	0.299299i
$379$	−17.0642	−	17.0642i	−0.876527	−	0.876527i	0.116646	−	0.993174i	$-0.462786\pi$
$379$	−17.0642	−	17.0642i	−0.876527	−	0.876527i	−0.993174	+	0.116646i	$0.962786\pi$
$380$	10.9310	+	12.8908i	0.560749	+	0.661285i
$381$	1.73382	−	1.73382i	0.0888264	−	0.0888264i
$382$	3.61470	−	8.40828i	0.184944	−	0.430205i
$383$	−0.228058	−	0.228058i	−0.0116532	−	0.0116532i	0.701256	−	0.712909i	$-0.252623\pi$
$383$	−0.228058	−	0.228058i	−0.0116532	−	0.0116532i	−0.712909	+	0.701256i	$0.752623\pi$
$384$	−27.5830	+	8.51755i	−1.40759	+	0.434659i
$385$	−19.1894	−	21.4453i	−0.977985	−	1.09295i
$386$	20.6457	−	8.23145i	1.05084	−	0.418970i
$387$			13.5022i			0.686354i
$388$	−0.377011	+	14.1561i	−0.0191398	+	0.718668i
$389$	−14.3036	+	14.3036i	−0.725221	+	0.725221i	−0.969664	−	0.244443i	$-0.921395\pi$
$389$	−14.3036	+	14.3036i	−0.725221	+	0.725221i	0.244443	+	0.969664i	$0.421395\pi$
$390$	−18.3707	+	6.16805i	−0.930237	+	0.312331i
$391$	−0.318794			−0.0161221
$392$	12.0910	−	4.45141i	0.610688	−	0.224830i
$393$	13.8771	+	13.8771i	0.700009	+	0.700009i
$394$	−14.0153	+	32.6015i	−0.706081	+	1.64244i
$395$	−12.9815	−	14.5075i	−0.653169	−	0.729953i
$396$	−26.5732	−	0.707707i	−1.33535	−	0.0355636i
$397$	5.11618			0.256774			0.128387	−	0.991724i	$-0.459020\pi$
$397$	5.11618			0.256774			0.128387	+	0.991724i	$0.459020\pi$
$398$	−10.4771	+	24.3711i	−0.525170	+	1.22161i
$399$	−32.7804			−1.64107
$400$	−19.7311	−	3.26863i	−0.986555	−	0.163431i
$401$	−16.2837			−0.813170			−0.406585	−	0.913613i	$-0.633281\pi$
$401$	−16.2837			−0.813170			−0.406585	+	0.913613i	$0.633281\pi$
$402$	15.1396	−	35.2168i	0.755096	−	1.75645i
$403$	3.97152			0.197835
$404$	−0.479742	+	18.0135i	−0.0238681	+	0.896207i
$405$	−10.7462	−	12.0095i	−0.533985	−	0.596758i
$406$	−10.6275	+	24.7210i	−0.527436	+	1.22688i
$407$	6.77518	+	6.77518i	0.335833	+	0.335833i
$408$	0.321175	−	0.695457i	0.0159005	−	0.0344303i
$409$	−17.4256			−0.861640			−0.430820	−	0.902438i	$-0.641776\pi$
$409$	−17.4256			−0.861640			−0.430820	+	0.902438i	$0.641776\pi$
$410$	5.12273	−	1.71998i	0.252993	−	0.0849438i
$411$	19.0732	−	19.0732i	0.940810	−	0.940810i
$412$	−5.47659	−	0.145854i	−0.269812	−	0.00718573i
$413$			25.4604i			1.25283i
$414$	−13.8514	+	5.52256i	−0.680758	+	0.271419i
$415$	16.5970	+	18.5481i	0.814714	+	0.910488i
$416$	12.1779	+	6.02239i	0.597073	+	0.295272i
$417$	29.4219	+	29.4219i	1.44080	+	1.44080i
$418$	7.99172	−	18.5898i	0.390888	−	0.909257i
$419$	−11.7257	+	11.7257i	−0.572837	+	0.572837i	−0.932920	−	0.360083i	$-0.882748\pi$
$419$	−11.7257	+	11.7257i	−0.572837	+	0.572837i	0.360083	+	0.932920i	$0.382748\pi$
$420$	29.5852	−	25.0874i	1.44361	−	1.22414i
$421$	−23.5406	−	23.5406i	−1.14730	−	1.14730i	−0.987082	−	0.160216i	$-0.948781\pi$
$421$	−23.5406	−	23.5406i	−1.14730	−	1.14730i	−0.160216	−	0.987082i	$-0.551219\pi$
$422$	−4.73206	−	11.8687i	−0.230353	−	0.577759i
$423$	7.55728	−	7.55728i	0.367447	−	0.367447i
$424$	1.26522	+	3.43661i	0.0614445	+	0.166896i
$425$	0.414505	−	0.331428i	0.0201064	−	0.0160766i
$426$	7.53608	+	3.23974i	0.365124	+	0.156966i
$427$	49.2335			2.38258
$428$	9.60186	+	10.1273i	0.464123	+	0.489521i
$429$	16.4052	+	16.4052i	0.792049	+	0.792049i
$430$	11.5296	−	3.87112i	0.556008	−	0.186682i
$431$		−	35.0243i		−	1.68706i	−0.537079	−	0.843532i	$-0.680472\pi$
$431$		−	35.0243i		−	1.68706i	0.537079	−	0.843532i	$-0.319528\pi$
$432$	0.277441	−	5.20503i	0.0133484	−	0.250427i
$433$	10.1094	−	10.1094i	0.485828	−	0.485828i	−0.421159	−	0.906987i	$-0.638376\pi$
$433$	10.1094	−	10.1094i	0.485828	−	0.485828i	0.906987	+	0.421159i	$0.138376\pi$
$434$	−7.38449	+	2.94420i	−0.354467	+	0.141326i
$435$	−1.77021	+	31.8872i	−0.0848752	+	1.52887i
$436$	−0.0209147	+	0.785311i	−0.00100163	+	0.0376096i
$437$		−	11.3509i		−	0.542985i
$438$	−18.8827	−	47.3605i	−0.902250	−	2.26297i
$439$			22.6071i			1.07898i	0.841993	+	0.539488i	$0.181382\pi$
$439$			22.6071i			1.07898i	−0.841993	+	0.539488i	$0.818618\pi$
$440$	7.01433	+	22.8940i	0.334395	+	1.09143i
$441$			15.9923i			0.761540i
$442$	−0.334872	+	0.133514i	−0.0159282	+	0.00635061i
$443$			10.9178i			0.518721i	0.965781	+	0.259360i	$0.0835118\pi$
$443$			10.9178i			0.518721i	−0.965781	+	0.259360i	$0.916488\pi$
$444$	−9.37241	+	8.88614i	−0.444795	+	0.421717i
$445$	23.3188	+	26.0601i	1.10542	+	1.23537i
$446$	3.18337	+	7.98436i	0.150737	+	0.378071i
$447$	−14.0638	+	14.0638i	−0.665195	+	0.665195i
$448$	−27.1078	−	2.16993i	−1.28072	−	0.102520i
$449$		−	28.8112i		−	1.35969i	−0.733358	−	0.679843i	$-0.762048\pi$
$449$		−	28.8112i		−	1.35969i	0.733358	−	0.679843i	$-0.237952\pi$
$450$	12.2685	−	21.5809i	0.578343	−	1.01733i
$451$	−4.57463	−	4.57463i	−0.215411	−	0.215411i
$452$	−24.7563	−	0.659318i	−1.16444	−	0.0310117i
$453$	10.5539			0.495865
$454$	16.2552	−	37.8117i	0.762893	−	1.77459i
$455$	−18.2270	−	1.01187i	−0.854495	−	0.0474371i
$456$	24.7622	+	11.4356i	1.15960	+	0.535522i
$457$	−19.1653	+	19.1653i	−0.896513	+	0.896513i	−0.995126	−	0.0986128i	$-0.968559\pi$
$457$	−19.1653	+	19.1653i	−0.896513	+	0.896513i	0.0986128	+	0.995126i	$0.468559\pi$
$458$	34.0727	−	13.5848i	1.59211	−	0.634778i
$459$	0.0978038	+	0.0978038i	0.00456509	+	0.00456509i
$460$	8.68700	+	10.2445i	0.405033	+	0.477651i
$461$	4.43227	−	4.43227i	0.206431	−	0.206431i	−0.596317	−	0.802749i	$-0.703370\pi$
$461$	4.43227	−	4.43227i	0.206431	−	0.206431i	0.802749	+	0.596317i	$0.203370\pi$
$462$	−42.6648	−	18.3415i	−1.98495	−	0.853324i
$463$	20.1518	+	20.1518i	0.936534	+	0.936534i	0.998103	−	0.0615691i	$-0.0196105\pi$
$463$	20.1518	+	20.1518i	0.936534	+	0.936534i	−0.0615691	+	0.998103i	$0.519610\pi$
$464$	16.6521	−	14.9667i	0.773052	−	0.694811i
$465$	−7.03120	+	6.29158i	−0.326064	+	0.291765i
$466$	−1.08634	−	2.72469i	−0.0503236	−	0.126219i
$467$		−	3.89858i		−	0.180405i	−0.995923	−	0.0902025i	$-0.971249\pi$
$467$		−	3.89858i		−	0.180405i	0.995923	−	0.0902025i	$-0.0287514\pi$
$468$	−12.2371	+	11.6022i	−0.565658	+	0.536310i
$469$	25.5342	−	25.5342i	1.17906	−	1.17906i
$470$	−8.61992	−	4.28652i	−0.397607	−	0.197723i
$471$	−51.7211			−2.38318
$472$	8.88200	−	19.2327i	0.408827	−	0.885256i
$473$	−10.2960	−	10.2960i	−0.473412	−	0.473412i
$474$	−28.8623	−	12.4079i	−1.32569	−	0.569912i
$475$	11.8007	+	14.7587i	0.541453	+	0.677175i
$476$	0.523671	−	0.496501i	0.0240024	−	0.0227571i
$477$	−4.54548			−0.208123
$478$	−16.2967	−	7.00590i	−0.745392	−	0.320443i
$479$	9.85299			0.450194			0.225097	−	0.974336i	$-0.427730\pi$
$479$	9.85299			0.450194			0.225097	+	0.974336i	$0.427730\pi$
$480$	−31.1004	+	8.62994i	−1.41953	+	0.393901i
$481$	6.07811			0.277138
$482$	−19.3418	−	8.31500i	−0.880994	−	0.378738i
$483$	−26.0510			−1.18536
$484$	4.83797	−	4.58696i	0.219908	−	0.208498i
$485$	−0.877595	+	15.8083i	−0.0398495	+	0.717818i
$486$	−28.9718	−	12.4549i	−1.31419	−	0.564966i
$487$	−13.9164	−	13.9164i	−0.630611	−	0.630611i	0.317610	−	0.948221i	$-0.397120\pi$
$487$	−13.9164	−	13.9164i	−0.630611	−	0.630611i	−0.948221	+	0.317610i	$0.897120\pi$
$488$	−37.1908	−	17.1754i	−1.68355	−	0.777492i
$489$	33.6392			1.52122
$490$	13.6560	−	4.58507i	0.616915	−	0.207132i
$491$	2.39213	−	2.39213i	0.107955	−	0.107955i	−0.651066	−	0.759021i	$-0.725678\pi$
$491$	2.39213	−	2.39213i	0.107955	−	0.107955i	0.759021	+	0.651066i	$0.225678\pi$
$492$	6.32829	−	5.99996i	0.285301	−	0.270499i
$493$			0.594124i			0.0267580i
$494$	−4.75384	−	11.9233i	−0.213885	−	0.536456i
$495$	−29.6746	−	1.64738i	−1.33377	−	0.0740443i
$496$	6.60531	+	0.352079i	0.296587	+	0.0158088i
$497$	5.46408	+	5.46408i	0.245098	+	0.245098i
$498$	36.9008	+	15.8636i	1.65357	+	0.710865i
$499$	−9.87034	+	9.87034i	−0.441857	+	0.441857i	−0.892636	−	0.450779i	$-0.851146\pi$
$499$	−9.87034	+	9.87034i	−0.441857	+	0.441857i	0.450779	+	0.892636i	$0.351146\pi$
$500$	−21.9455	−	4.28886i	−0.981433	−	0.191804i
$501$	30.1575	+	30.1575i	1.34734	+	1.34734i
$502$	10.0034	−	3.98837i	0.446474	−	0.178010i
$503$	9.29035	−	9.29035i	0.414236	−	0.414236i	−0.468975	−	0.883211i	$-0.655377\pi$
$503$	9.29035	−	9.29035i	0.414236	−	0.414236i	0.883211	+	0.468975i	$0.155377\pi$
$504$	14.1521	−	30.6443i	0.630384	−	1.36501i
$505$	−1.11673	+	20.1159i	−0.0496939	+	0.895146i
$506$	6.35110	−	14.7735i	0.282341	−	0.656763i
$507$	−18.4536			−0.819553
$508$	−1.92124	−	0.0511671i	−0.0852413	−	0.00227017i
$509$	−6.53818	−	6.53818i	−0.289800	−	0.289800i	0.547201	−	0.837001i	$-0.315693\pi$
$509$	−6.53818	−	6.53818i	−0.289800	−	0.289800i	−0.837001	+	0.547201i	$0.815693\pi$
$510$	0.381350	−	0.766870i	0.0168865	−	0.0339576i
$511$		−	48.0301i		−	2.12473i
$512$	19.7201	+	11.0958i	0.871513	+	0.490372i
$513$	−3.48236	+	3.48236i	−0.153750	+	0.153750i
$514$	2.87878	+	7.22040i	0.126978	+	0.318478i
$515$	−6.11577	−	0.339516i	−0.269493	−	0.0149608i
$516$	14.2429	−	13.5040i	0.627011	−	0.594480i
$517$			11.5255i			0.506893i
$518$	−11.3014	+	4.50588i	−0.496555	+	0.197977i
$519$			39.7445i			1.74459i
$520$	13.4156	+	7.12294i	0.588312	+	0.312362i
$521$			14.2961i			0.626324i	0.949700	+	0.313162i	$0.101388\pi$
$521$			14.2961i			0.626324i	−0.949700	+	0.313162i	$0.898612\pi$
$522$	10.2922	+	25.8143i	0.450476	+	1.12986i
$523$		−	16.0319i		−	0.701027i	−0.936558	−	0.350513i	$-0.886007\pi$
$523$		−	16.0319i		−	0.701027i	0.936558	−	0.350513i	$-0.113993\pi$
$524$	0.409530	−	15.3772i	0.0178904	−	0.671756i
$525$	33.8721	−	27.0834i	1.47830	−	1.18201i
$526$	−31.5187	+	12.5665i	−1.37428	+	0.547928i
$527$	−0.124115	+	0.124115i	−0.00540655	+	0.00540655i
$528$	25.8302	+	28.7389i	1.12412	+	1.25070i
$529$			13.9794i			0.607798i
$530$	1.30321	+	3.88143i	0.0566077	+	0.168598i
$531$	18.5932	+	18.5932i	0.806875	+	0.806875i
$532$	17.6782	+	18.6456i	0.766448	+	0.808390i
$533$	−4.10397			−0.177762
$534$	51.8458	+	22.2884i	2.24359	+	0.964514i
$535$	10.4043	+	11.6274i	0.449819	+	0.502697i
$536$	−28.1961	+	10.3807i	−1.21789	+	0.448376i
$537$	39.7957	−	39.7957i	1.71731	−	1.71731i
$538$	−1.89236	−	4.74631i	−0.0815854	−	0.204628i
$539$	−12.1949	−	12.1949i	−0.525271	−	0.525271i
$540$	0.477820	−	5.80804i	0.0205621	−	0.249938i
$541$	−14.3926	+	14.3926i	−0.618785	+	0.618785i	−0.945220	−	0.326435i	$-0.894153\pi$
$541$	−14.3926	+	14.3926i	−0.618785	+	0.618785i	0.326435	+	0.945220i	$0.394153\pi$
$542$	−1.86376	+	4.33536i	−0.0800555	+	0.186220i
$543$	−7.62178	−	7.62178i	−0.327082	−	0.327082i
$544$	−0.568785	+	0.192369i	−0.0243865	+	0.00824777i
$545$	−0.0486846	+	0.876965i	−0.00208542	+	0.0375651i
$546$	−27.3648	+	10.9104i	−1.17111	+	0.466921i
$547$		−	11.6741i		−	0.499148i	−0.968356	−	0.249574i	$-0.919709\pi$
$547$		−	11.6741i		−	0.499148i	0.968356	−	0.249574i	$-0.0802905\pi$
$548$	−21.1349	−	0.562871i	−0.902838	−	0.0240447i
$549$	35.9541	−	35.9541i	1.53448	−	1.53448i
$550$	7.10111	+	25.8117i	0.302792	+	1.10061i
$551$	−21.1541			−0.901197
$552$	19.6788	+	9.08801i	0.837584	+	0.386811i
$553$	−20.9268	−	20.9268i	−0.889898	−	0.889898i
$554$	2.57340	−	5.98608i	0.109333	−	0.254324i
$555$	−10.7607	+	9.62880i	−0.456767	+	0.408720i
$556$	0.868274	−	32.6023i	0.0368230	−	1.38264i
$557$	−39.6712			−1.68092			−0.840460	−	0.541873i	$-0.817715\pi$
$557$	−39.6712			−1.68092			−0.840460	+	0.541873i	$0.817715\pi$
$558$	−3.24264	+	7.54281i	−0.137272	+	0.319313i
$559$	−9.23671			−0.390671
$560$	−30.2249	−	3.29875i	−1.27723	−	0.139398i
$561$	−1.02537			−0.0432911
$562$	−12.3537	+	28.7364i	−0.521110	+	1.21217i
$563$	−12.4534			−0.524850			−0.262425	−	0.964952i	$-0.584522\pi$
$563$	−12.4534			−0.524850			−0.262425	+	0.964952i	$0.584522\pi$
$564$	−15.5302	−	0.413605i	−0.653939	−	0.0174159i
$565$	−27.6456	−	1.53474i	−1.16306	−	0.0645671i
$566$	6.06740	−	14.1136i	0.255032	−	0.593238i
$567$	−17.3235	−	17.3235i	−0.727519	−	0.727519i
$568$	−2.22137	−	6.03371i	−0.0932066	−	0.253169i
$569$	−5.62622			−0.235863			−0.117932	−	0.993022i	$-0.537626\pi$
$569$	−5.62622			−0.235863			−0.117932	+	0.993022i	$0.537626\pi$
$570$	27.3049	+	13.5782i	1.14368	+	0.568728i
$571$	23.1808	−	23.1808i	0.970086	−	0.970086i	−0.0294797	−	0.999565i	$-0.509385\pi$
$571$	23.1808	−	23.1808i	0.970086	−	0.970086i	0.999565	+	0.0294797i	$0.00938505\pi$
$572$	0.484136	−	18.1785i	0.0202427	−	0.760081i
$573$		−	16.5132i		−	0.689848i
$574$	7.63076	−	3.04239i	0.318502	−	0.126987i
$575$	9.37814	+	11.7289i	0.391095	+	0.489128i
$576$	−21.3808	+	18.2115i	−0.890869	+	0.758814i
$577$	−25.6307	−	25.6307i	−1.06702	−	1.06702i	−0.997587	−	0.0694322i	$-0.977881\pi$
$577$	−25.6307	−	25.6307i	−1.06702	−	1.06702i	−0.0694322	−	0.997587i	$-0.522119\pi$
$578$	−9.48892	+	22.0725i	−0.394687	+	0.918094i
$579$	28.3562	−	28.3562i	1.17844	−	1.17844i
$580$	19.0922	−	16.1896i	0.792761	−	0.672237i
$581$	26.7552	+	26.7552i	1.10999	+	1.10999i
$582$	9.46259	+	23.7335i	0.392237	+	0.983787i
$583$	3.46614	−	3.46614i	0.143553	−	0.143553i
$584$	−16.7555	+	36.2817i	−0.693349	+	1.50135i
$585$	−14.0497	+	12.5718i	−0.580884	+	0.519780i
$586$	23.9147	+	10.2809i	0.987908	+	0.424700i
$587$	25.5579			1.05489			0.527444	−	0.849590i	$-0.323151\pi$
$587$	25.5579			1.05489			0.527444	+	0.849590i	$0.323151\pi$
$588$	16.8697	−	15.9945i	0.695696	−	0.659602i
$589$	−4.41920	−	4.41920i	−0.182090	−	0.182090i
$590$	10.5461	−	21.2076i	0.434177	−	0.873103i
$591$			64.0266i			2.63370i
$592$	10.1089	+	0.538831i	0.415474	+	0.0221458i
$593$	2.96607	−	2.96607i	0.121802	−	0.121802i	−0.643578	−	0.765380i	$-0.722551\pi$
$593$	2.96607	−	2.96607i	0.121802	−	0.121802i	0.765380	+	0.643578i	$0.222551\pi$
$594$	−6.48088	+	2.58393i	−0.265914	+	0.106020i
$595$	0.601241	−	0.537996i	0.0246485	−	0.0220557i
$596$	15.5840	+	0.415039i	0.638347	+	0.0170007i
$597$			47.8629i			1.95890i
$598$	−3.77793	−	9.47559i	−0.154491	−	0.387486i
$599$			5.14724i			0.210311i	0.994456	+	0.105155i	$0.0335340\pi$
$599$			5.14724i			0.210311i	−0.994456	+	0.105155i	$0.966466\pi$
$600$	−35.0350	+	8.64217i	−1.43030	+	0.352815i
$601$		−	33.5619i		−	1.36902i	−0.729005	−	0.684509i	$-0.760017\pi$
$601$		−	33.5619i		−	1.36902i	0.729005	−	0.684509i	$-0.239983\pi$
$602$	17.1744	−	6.84745i	0.699976	−	0.279081i
$603$		−	37.2940i		−	1.51873i
$604$	−5.69163	−	6.00309i	−0.231589	−	0.244262i
$605$	5.55461	−	4.97032i	0.225827	−	0.202072i
$606$	12.0411	+	30.2007i	0.489134	+	1.22682i
$607$	−3.29572	+	3.29572i	−0.133769	+	0.133769i	−0.770821	−	0.637052i	$-0.780154\pi$
$607$	−3.29572	+	3.29572i	−0.133769	+	0.133769i	0.637052	+	0.770821i	$0.280154\pi$
$608$	−6.84943	−	20.2519i	−0.277781	−	0.821325i
$609$			48.5501i			1.96735i
$610$	−41.0097	−	20.3933i	−1.66043	−	0.825702i
$611$	5.16986	+	5.16986i	0.209150	+	0.209150i
$612$	0.0198413	−	0.745008i	0.000802037	−	0.0301152i
$613$	0.261903			0.0105781			0.00528907	−	0.999986i	$-0.498316\pi$
$613$	0.261903			0.0105781			0.00528907	+	0.999986i	$0.498316\pi$
$614$	−3.69125	+	8.58633i	−0.148967	+	0.346516i
$615$	7.26568	−	6.50140i	0.292981	−	0.262162i
$616$	12.5761	+	34.1593i	0.506704	+	1.37632i
$617$	12.1529	−	12.1529i	0.489259	−	0.489259i	−0.418813	−	0.908072i	$-0.637554\pi$
$617$	12.1529	−	12.1529i	0.489259	−	0.489259i	0.908072	+	0.418813i	$0.137554\pi$
$618$	−9.18181	+	3.66080i	−0.369347	+	0.147259i
$619$	−12.1134	−	12.1134i	−0.486877	−	0.486877i	0.420442	−	0.907319i	$-0.361875\pi$
$619$	−12.1134	−	12.1134i	−0.486877	−	0.486877i	−0.907319	+	0.420442i	$0.861875\pi$
$620$	7.37054	+	0.606366i	0.296008	+	0.0243522i
$621$	−2.76747	+	2.76747i	−0.111055	+	0.111055i
$622$	0.787474	+	0.338534i	0.0315748	+	0.0135740i
$623$	37.5911	+	37.5911i	1.50606	+	1.50606i
$624$	24.4774	+	1.30470i	0.979880	+	0.0522300i
$625$	−24.3874	−	5.50042i	−0.975496	−	0.220017i
$626$	−14.3479	−	35.9867i	−0.573459	−	1.43832i
$627$		−	36.5089i		−	1.45802i
$628$	27.8928	+	29.4191i	1.11304	+	1.17395i
$629$	−0.189949	+	0.189949i	−0.00757377	+	0.00757377i
$630$	16.8036	−	33.7910i	0.669472	−	1.34627i
$631$	49.8568			1.98477			0.992384	−	0.123179i	$-0.0393090\pi$
$631$	49.8568			1.98477			0.992384	+	0.123179i	$0.0393090\pi$
$632$	8.50759	+	23.1084i	0.338414	+	0.919204i
$633$	−16.3013	−	16.3013i	−0.647917	−	0.647917i
$634$	9.15093	+	3.93397i	0.363430	+	0.156238i
$635$	−2.14547	−	0.119105i	−0.0851404	−	0.00472656i
$636$	4.54609	+	4.79486i	0.180264	+	0.190129i
$637$	−10.9402			−0.433467
$638$	−27.5328	−	11.8363i	−1.09003	−	0.468604i
$639$	7.98059			0.315707
$640$	21.6810	+	13.0360i	0.857015	+	0.515292i
$641$	−4.10036			−0.161954			−0.0809772	−	0.996716i	$-0.525804\pi$
$641$	−4.10036			−0.161954			−0.0809772	+	0.996716i	$0.525804\pi$
$642$	23.1324	+	9.94459i	0.912964	+	0.392482i
$643$	−18.7451			−0.739233			−0.369617	−	0.929184i	$-0.620511\pi$
$643$	−18.7451			−0.739233			−0.369617	+	0.929184i	$0.620511\pi$
$644$	14.0491	+	14.8179i	0.553611	+	0.583906i
$645$	16.3527	−	14.6326i	0.643888	−	0.576157i
$646$	0.521184	+	0.224056i	0.0205057	+	0.00881537i
$647$	5.46529	+	5.46529i	0.214863	+	0.214863i	0.806330	−	0.591467i	$-0.201451\pi$
$647$	5.46529	+	5.46529i	0.214863	+	0.214863i	−0.591467	+	0.806330i	$0.701451\pi$
$648$	7.04270	+	19.1295i	0.276663	+	0.751477i
$649$	−28.3563			−1.11308
$650$	14.7633	+	8.39277i	0.579063	+	0.329192i
$651$	−10.1424	+	10.1424i	−0.397510	+	0.397510i
$652$	−18.1414	−	19.1341i	−0.710471	−	0.749350i
$653$			33.9219i			1.32747i	0.747970	+	0.663733i	$0.231029\pi$
$653$			33.9219i			1.32747i	−0.747970	+	0.663733i	$0.768971\pi$
$654$	0.524937	+	1.31662i	0.0205267	+	0.0514838i
$655$	0.953294	−	17.1719i	0.0372483	−	0.670961i
$656$	−6.82559	−	0.363821i	−0.266495	−	0.0142048i
$657$	−35.0753	−	35.0753i	−1.36842	−	1.36842i
$658$	−13.4452	−	5.78007i	−0.524149	−	0.225331i
$659$	26.4961	−	26.4961i	1.03214	−	1.03214i	0.0326746	−	0.999466i	$-0.489598\pi$
$659$	26.4961	−	26.4961i	1.03214	−	1.03214i	0.999466	−	0.0326746i	$-0.0104025\pi$
$660$	27.9408	+	32.9503i	1.08760	+	1.28259i
$661$	10.6974	+	10.6974i	0.416081	+	0.416081i	0.883851	−	0.467769i	$-0.154942\pi$
$661$	10.6974	+	10.6974i	0.416081	+	0.416081i	−0.467769	+	0.883851i	$0.654942\pi$
$662$	24.5738	−	9.79759i	0.955087	−	0.380794i
$663$	−0.459936	+	0.459936i	−0.0178624	+	0.0178624i
$664$	−10.8771	−	29.5444i	−0.422112	−	1.14655i
$665$	19.1557	+	21.4075i	0.742826	+	0.830149i
$666$	−4.96262	+	11.5437i	−0.192297	+	0.447309i
$667$	−16.8114			−0.650941
$668$	0.889984	−	33.4174i	0.0344345	−	1.29296i
$669$	10.9663	+	10.9663i	0.423980	+	0.423980i
$670$	−31.8457	+	10.6923i	−1.23031	+	0.413081i
$671$			54.8333i			2.11682i
$672$	−46.4795	+	15.7199i	−1.79299	+	0.606408i
$673$	−6.70854	+	6.70854i	−0.258595	+	0.258595i	−0.824483	−	0.565887i	$-0.808534\pi$
$673$	−6.70854	+	6.70854i	−0.258595	+	0.258595i	0.565887	+	0.824483i	$0.308534\pi$
$674$	−5.72774	−	14.3660i	−0.220624	−	0.553358i
$675$	0.721194	−	6.47549i	0.0277588	−	0.249242i
$676$	9.95188	+	10.4965i	0.382764	+	0.403710i
$677$			13.1970i			0.507200i	0.967309	+	0.253600i	$0.0816147\pi$
$677$			13.1970i			0.507200i	−0.967309	+	0.253600i	$0.918385\pi$
$678$	−41.5053	+	16.5482i	−1.59400	+	0.635530i
$679$			24.0691i			0.923686i
$680$	−0.641857	+	0.196654i	−0.0246141	+	0.00754134i
$681$		−	74.2591i		−	2.84561i
$682$	−3.27908	−	8.22440i	−0.125562	−	0.314928i
$683$			37.9089i			1.45054i	0.688462	+	0.725272i	$0.258286\pi$
$683$			37.9089i			1.45054i	−0.688462	+	0.725272i	$0.741714\pi$
$684$	26.5265	+	0.706462i	1.01427	+	0.0270122i
$685$	−23.6016	−	1.31024i	−0.901770	−	0.0500616i
$686$	−10.9168	+	4.35252i	−0.416804	+	0.166180i
$687$	46.7978	−	46.7978i	1.78545	−	1.78545i
$688$	−15.3622	−	0.818844i	−0.585679	−	0.0312181i
$689$		−	3.10952i		−	0.118463i
$690$	21.6995	+	10.7907i	0.826085	+	0.410796i
$691$	20.8280	+	20.8280i	0.792335	+	0.792335i	0.981873	−	0.189538i	$-0.0606991\pi$
$691$	20.8280	+	20.8280i	0.792335	+	0.792335i	−0.189538	+	0.981873i	$0.560699\pi$
$692$	22.6068	−	21.4339i	0.859382	−	0.814794i
$693$	−45.1813			−1.71630
$694$	14.8043	+	6.36433i	0.561962	+	0.241586i
$695$	2.02114	−	36.4073i	0.0766664	−	1.38101i
$696$	16.9370	−	36.6745i	0.641994	−	1.39015i
$697$	0.128255	−	0.128255i	0.00485799	−	0.00485799i
$698$	8.92605	+	22.3878i	0.337856	+	0.847392i
$699$	−3.74227	−	3.74227i	−0.141546	−	0.141546i
$700$	−33.6721	−	4.66075i	−1.27269	−	0.176160i
$701$	19.9053	−	19.9053i	0.751812	−	0.751812i	−0.223005	−	0.974817i	$-0.571587\pi$
$701$	19.9053	−	19.9053i	0.751812	−	0.751812i	0.974817	+	0.223005i	$0.0715868\pi$
$702$	−1.74800	+	4.06609i	−0.0659741	+	0.153465i
$703$	−6.76326	−	6.76326i	−0.255081	−	0.255081i
$704$	2.41674	−	30.1910i	0.0910844	−	1.13787i
$705$	−17.3427	−	0.962778i	−0.653165	−	0.0362603i
$706$	12.0361	−	4.79882i	0.452986	−	0.180606i
$707$			30.6277i			1.15187i
$708$	1.01759	−	38.2089i	0.0382435	−	1.43598i
$709$	−8.57112	+	8.57112i	−0.321895	+	0.321895i	−0.849494	−	0.527599i	$-0.823092\pi$
$709$	−8.57112	+	8.57112i	−0.321895	+	0.321895i	0.527599	+	0.849494i	$0.323092\pi$
$710$	−2.28806	−	6.81469i	−0.0858695	−	0.255751i
$711$	−30.5647			−1.14627
$712$	−15.2823	−	41.5100i	−0.572729	−	1.55565i
$713$	−3.51199	−	3.51199i	−0.131525	−	0.131525i
$714$	0.514224	−	1.19615i	0.0192443	−	0.0447649i
$715$	1.12696	−	20.3001i	0.0421458	−	0.759182i
$716$	−44.0975	−	1.17442i	−1.64800	−	0.0438901i
$717$	−32.0053			−1.19526
$718$	−1.81581	+	4.22382i	−0.0677655	+	0.157631i
$719$	−33.1900			−1.23778			−0.618889	−	0.785478i	$-0.712417\pi$
$719$	−33.1900			−1.23778			−0.618889	+	0.785478i	$0.712417\pi$
$720$	−24.4815	+	19.6635i	−0.912373	+	0.732817i
$721$	−9.31162			−0.346783
$722$	2.63464	−	6.12852i	0.0980511	−	0.228080i
$723$	−37.9857			−1.41270
$724$	−0.224927	+	8.44566i	−0.00835936	+	0.313880i
$725$	21.8587	−	17.4777i	0.811810	−	0.649104i
$726$	4.75069	−	11.0507i	0.176315	−	0.410131i
$727$	5.06503	+	5.06503i	0.187852	+	0.187852i	0.794767	−	0.606915i	$-0.207593\pi$
$727$	5.06503	+	5.06503i	0.187852	+	0.187852i	−0.606915	+	0.794767i	$0.707593\pi$
$728$	20.9635	+	9.68131i	0.776958	+	0.358813i
$729$	−35.2770			−1.30655
$730$	−19.8949	+	40.0073i	−0.736341	+	1.48074i
$731$	0.288660	−	0.288660i	0.0106765	−	0.0106765i
$732$	−73.8856	−	1.96775i	−2.73089	−	0.0727300i
$733$		−	43.0744i		−	1.59099i	−0.605961	−	0.795494i	$-0.707211\pi$
$733$		−	43.0744i		−	1.59099i	0.605961	−	0.795494i	$-0.292789\pi$
$734$	23.6009	−	9.40969i	0.871124	−	0.347318i
$735$	19.3686	−	17.3312i	0.714422	−	0.639272i
$736$	−5.44332	−	16.0944i	−0.200643	−	0.593249i
$737$	28.4384	+	28.4384i	1.04754	+	1.04754i
$738$	3.35078	−	7.79436i	0.123344	−	0.286914i
$739$	11.3838	−	11.3838i	0.418762	−	0.418762i	−0.466015	−	0.884777i	$-0.654311\pi$
$739$	11.3838	−	11.3838i	0.418762	−	0.418762i	0.884777	+	0.466015i	$0.154311\pi$
$740$	11.2801	+	0.927997i	0.414663	+	0.0341138i
$741$	−16.3763	−	16.3763i	−0.601599	−	0.601599i
$742$	2.30518	+	5.78173i	0.0846258	+	0.212254i
$743$	1.54795	−	1.54795i	0.0567888	−	0.0567888i	−0.678142	−	0.734931i	$-0.737215\pi$
$743$	1.54795	−	1.54795i	0.0567888	−	0.0567888i	0.734931	+	0.678142i	$0.237215\pi$
$744$	11.1997	−	4.12328i	0.410601	−	0.151167i
$745$	17.4029	+	0.966116i	0.637591	+	0.0353958i
$746$	−28.5523	−	12.2746i	−1.04537	−	0.449404i
$747$	39.0774			1.42977
$748$	0.552973	+	0.583233i	0.0202187	+	0.0213251i
$749$	16.7723	+	16.7723i	0.612847	+	0.612847i
$750$	−39.4326	+	8.52903i	−1.43988	+	0.311436i
$751$			1.49244i			0.0544600i	0.999629	+	0.0272300i	$0.00866865\pi$
$751$			1.49244i			0.0544600i	−0.999629	+	0.0272300i	$0.991331\pi$
$752$	8.14005	+	9.05667i	0.296837	+	0.330263i
$753$	13.7394	−	13.7394i	0.500690	−	0.500690i
$754$	−17.6593	+	7.04078i	−0.643113	+	0.256410i
$755$	−6.16731	−	6.89231i	−0.224451	−	0.250837i
$756$	0.235861	−	8.85618i	0.00857817	−	0.322096i
$757$		−	22.7030i		−	0.825154i	−0.910923	−	0.412577i	$-0.864629\pi$
$757$		−	22.7030i		−	0.825154i	0.910923	−	0.412577i	$-0.135371\pi$
$758$	12.6394	+	31.7015i	0.459085	+	1.15145i
$759$		−	29.0140i		−	1.05314i
$760$	−7.00198	−	22.8537i	−0.253989	−	0.828991i
$761$			33.6599i			1.22017i	0.792335	+	0.610086i	$0.208865\pi$
$761$			33.6599i			1.22017i	−0.792335	+	0.610086i	$0.791135\pi$
$762$	−3.22107	+	1.28424i	−0.116687	+	0.0465232i
$763$			1.33523i			0.0483386i
$764$	−9.39275	+	8.90543i	−0.339818	+	0.322187i
$765$	0.0461860	−	0.831959i	0.00166986	−	0.0300795i
$766$	0.168923	+	0.423683i	0.00610343	+	0.0153083i
$767$	−12.7194	+	12.7194i	−0.459271	+	0.459271i
$768$	40.5944	+	4.33989i	1.46482	+	0.156602i
$769$			10.1943i			0.367615i	0.982962	+	0.183808i	$0.0588423\pi$
$769$			10.1943i			0.367615i	−0.982962	+	0.183808i	$0.941158\pi$
$770$	12.9537	+	38.5807i	0.466817	+	1.39035i
$771$	9.91699	+	9.91699i	0.357152	+	0.357152i
$772$	−31.4213	−	0.836823i	−1.13088	−	0.0301179i
$773$	7.34419			0.264152			0.132076	−	0.991240i	$-0.457836\pi$
$773$	7.34419			0.264152			0.132076	+	0.991240i	$0.457836\pi$
$774$	7.54153	−	17.5426i	0.271075	−	0.630556i
$775$	8.21755	+	0.915212i	0.295183	+	0.0328754i
$776$	8.39662	−	18.1817i	0.301421	−	0.652684i
$777$	−15.5221	+	15.5221i	−0.556853	+	0.556853i
$778$	26.5730	−	10.5947i	0.952688	−	0.379838i
$779$	4.56658	+	4.56658i	0.163615	+	0.163615i
$780$	27.3131	+	2.24702i	0.977967	+	0.0804561i
$781$	−6.08556	+	6.08556i	−0.217759	+	0.217759i
$782$	0.414191	+	0.178060i	0.0148114	+	0.00636741i
$783$	5.15763	+	5.15763i	0.184319	+	0.184319i
$784$	−18.1954	−	0.969861i	−0.649837	−	0.0346379i
$785$	30.2239	+	33.7769i	1.07874	+	1.20555i
$786$	−10.2788	−	25.7807i	−0.366633	−	0.919568i
$787$			29.4359i			1.04928i	0.851326	+	0.524638i	$0.175799\pi$
$787$			29.4359i			1.04928i	−0.851326	+	0.524638i	$0.824201\pi$
$788$	36.4186	−	34.5291i	1.29736	−	1.23005i
$789$	−43.2900	+	43.2900i	−1.54116	+	1.54116i
$790$	8.76302	+	26.0995i	0.311774	+	0.928578i
$791$	−42.0921			−1.49662
$792$	34.1298	+	15.7617i	1.21275	+	0.560069i
$793$	24.5959	+	24.5959i	0.873425	+	0.873425i
$794$	−6.64715	−	2.85760i	−0.235899	−	0.101412i
$795$	4.92603	+	5.50511i	0.174708	+	0.195246i
$796$	27.2246	−	25.8121i	0.964950	−	0.914886i
$797$	50.3934			1.78503			0.892513	−	0.451022i	$-0.148940\pi$
$797$	50.3934			1.78503			0.892513	+	0.451022i	$0.148940\pi$
$798$	42.5897	+	18.3092i	1.50766	+	0.648140i
$799$	−0.323131			−0.0114315
$800$	23.8098	+	15.2674i	0.841804	+	0.539784i
$801$	54.9039			1.93993
$802$	21.1565	+	9.09514i	0.747062	+	0.321161i
$803$	53.4930			1.88773
$804$	−39.3401	+	37.2990i	−1.38742	+	1.31544i
$805$	15.2232	+	17.0128i	0.536548	+	0.599623i
$806$	−5.15996	−	2.21826i	−0.181752	−	0.0781348i
$807$	−6.51890	−	6.51890i	−0.229476	−	0.229476i
$808$	10.6846	−	23.1360i	0.375884	−	0.813922i
$809$	−27.1588			−0.954851			−0.477426	−	0.878672i	$-0.658430\pi$
$809$	−27.1588			−0.954851			−0.477426	+	0.878672i	$0.658430\pi$
$810$	7.25415	+	21.6055i	0.254885	+	0.759140i
$811$	−11.5416	+	11.5416i	−0.405280	+	0.405280i	−0.880089	−	0.474809i	$-0.842517\pi$
$811$	−11.5416	+	11.5416i	−0.405280	+	0.405280i	0.474809	+	0.880089i	$0.342517\pi$
$812$	27.6155	−	26.1827i	0.969113	−	0.918833i
$813$			8.51429i			0.298609i
$814$	−5.01838	−	12.5868i	−0.175894	−	0.441168i
$815$	−19.6575	−	21.9684i	−0.688574	−	0.769520i
$816$	−0.805726	+	0.724178i	−0.0282060	+	0.0253513i
$817$	10.2779	+	10.2779i	0.359579	+	0.359579i
$818$	22.6401	+	9.73292i	0.791591	+	0.340304i
$819$	−20.2664	+	20.2664i	−0.708166	+	0.708166i
$820$	−7.61635	−	0.626587i	−0.265974	−	0.0218814i
$821$	−20.2900	−	20.2900i	−0.708126	−	0.708126i	0.258015	−	0.966141i	$-0.416932\pi$
$821$	−20.2900	−	20.2900i	−0.708126	−	0.708126i	−0.966141	+	0.258015i	$0.916932\pi$
$822$	−35.4338	+	14.1275i	−1.23590	+	0.492754i
$823$	−31.4540	+	31.4540i	−1.09642	+	1.09642i	−0.101592	+	0.994826i	$0.532394\pi$
$823$	−31.4540	+	31.4540i	−1.09642	+	1.09642i	−0.994826	+	0.101592i	$0.967606\pi$
$824$	7.03395	+	3.24840i	0.245039	+	0.113164i
$825$	30.1638	+	37.7247i	1.05017	+	1.31341i
$826$	14.2207	−	33.0793i	0.494802	−	1.15098i
$827$	15.3304			0.533090			0.266545	−	0.963822i	$-0.414118\pi$
$827$	15.3304			0.533090			0.266545	+	0.963822i	$0.414118\pi$
$828$	21.0809	+	0.561433i	0.732611	+	0.0195111i
$829$	−0.896046	−	0.896046i	−0.0311210	−	0.0311210i	0.691375	−	0.722496i	$-0.257005\pi$
$829$	−0.896046	−	0.896046i	−0.0311210	−	0.0311210i	−0.722496	+	0.691375i	$0.757005\pi$
$830$	−11.2036	−	33.3685i	−0.388884	−	1.15824i
$831$		−	11.7562i		−	0.407817i
$832$	−12.4583	−	14.6264i	−0.431915	−	0.507080i
$833$	0.341897	−	0.341897i	0.0118460	−	0.0118460i
$834$	−21.7928	−	54.6595i	−0.754623	−	1.89270i
$835$	2.07168	−	37.3176i	0.0716935	−	1.29143i
$836$	−20.7664	+	19.6889i	−0.718220	+	0.680956i
$837$			2.15491i			0.0744845i
$838$	21.7838	−	8.68522i	0.752508	−	0.300026i
$839$			48.1891i			1.66367i	0.555021	+	0.831837i	$0.312710\pi$
$839$			48.1891i			1.66367i	−0.555021	+	0.831837i	$0.687290\pi$
$840$	−52.4508	+	16.0700i	−1.80972	+	0.554468i
$841$			2.33080i			0.0803723i
$842$	17.4365	+	43.7333i	0.600902	+	1.50715i
$843$			56.4359i			1.94376i
$844$	−0.481069	+	18.0634i	−0.0165591	+	0.621767i
$845$	10.7836	+	12.0513i	0.370967	+	0.414577i
$846$	−14.0398	+	5.59768i	−0.482698	+	0.192452i
$847$	8.01241	−	8.01241i	0.275310	−	0.275310i
$848$	0.275662	−	5.17166i	0.00946628	−	0.177596i
$849$		−	27.7179i		−	0.951277i
$850$	−0.723658	+	0.199087i	−0.0248213	+	0.00682863i
$851$	−5.37484	−	5.37484i	−0.184247	−	0.184247i
$852$	−7.98166	−	8.41843i	−0.273447	−	0.288411i
$853$	−13.7426			−0.470537			−0.235268	−	0.971930i	$-0.575597\pi$
$853$	−13.7426			−0.470537			−0.235268	+	0.971930i	$0.575597\pi$
$854$	−63.9663	−	27.4990i	−2.18888	−	0.940996i
$855$	29.6224	+	1.64448i	1.01306	+	0.0562401i
$856$	−6.81862	−	18.5208i	−0.233056	−	0.633029i
$857$	−13.4366	+	13.4366i	−0.458986	+	0.458986i	−0.898323	−	0.439336i	$-0.855214\pi$
$857$	−13.4366	+	13.4366i	−0.458986	+	0.458986i	0.439336	+	0.898323i	$0.355214\pi$
$858$	−12.1513	−	30.4773i	−0.414839	−	1.04048i
$859$	7.00719	+	7.00719i	0.239082	+	0.239082i	0.816470	−	0.577388i	$-0.195928\pi$
$859$	7.00719	+	7.00719i	0.239082	+	0.239082i	−0.577388	+	0.816470i	$0.695928\pi$
$860$	−17.1420	−	1.41025i	−0.584536	−	0.0480890i
$861$	10.4806	−	10.4806i	0.357178	−	0.357178i
$862$	−19.5626	+	45.5051i	−0.666304	+	1.54991i
$863$	−41.4708	−	41.4708i	−1.41168	−	1.41168i	−0.748123	−	0.663560i	$-0.769045\pi$
$863$	−41.4708	−	41.4708i	−1.41168	−	1.41168i	−0.663560	−	0.748123i	$-0.730955\pi$
$864$	−3.26769	+	6.60763i	−0.111169	+	0.224796i
$865$	25.9555	−	23.2252i	0.882513	−	0.789682i
$866$	−18.7811	+	7.48806i	−0.638209	+	0.254455i
$867$			43.3486i			1.47219i
$868$	11.2387	+	0.299313i	0.381466	+	0.0101593i
$869$	23.3070	−	23.3070i	0.790636	−	0.790636i
$870$	20.1103	−	40.4405i	0.681802	−	1.37106i
$871$	25.5125			0.864458
$872$	0.465802	−	1.00863i	0.0157741	−	0.0341564i
$873$	17.5771	+	17.5771i	0.594894	+	0.594894i
$874$	−6.33993	+	14.7475i	−0.214451	+	0.498842i
$875$	−37.4807	−	6.29398i	−1.26708	−	0.212775i
$876$	−1.91965	+	72.0796i	−0.0648588	+	2.43534i
$877$	−5.34168			−0.180376			−0.0901879	−	0.995925i	$-0.528747\pi$
$877$	−5.34168			−0.180376			−0.0901879	+	0.995925i	$0.528747\pi$
$878$	12.6270	−	29.3721i	0.426141	−	0.991259i
$879$	46.9666			1.58414
$880$	3.67395	−	33.6627i	0.123849	−	1.13477i
$881$	−45.9723			−1.54885			−0.774423	−	0.632668i	$-0.781960\pi$
$881$	−45.9723			−1.54885			−0.774423	+	0.632668i	$0.781960\pi$
$882$	8.93240	−	20.7779i	0.300769	−	0.699630i
$883$	2.64739			0.0890918			0.0445459	−	0.999007i	$-0.485816\pi$
$883$	2.64739			0.0890918			0.0445459	+	0.999007i	$0.485816\pi$
$884$	0.509653	+	0.0135732i	0.0171415	+	0.000456518i
$885$	2.36872	−	42.6683i	0.0796238	−	1.43428i
$886$	6.09806	−	14.1849i	0.204868	−	0.476551i
$887$	3.87171	+	3.87171i	0.129999	+	0.129999i	0.769113	−	0.639113i	$-0.220699\pi$
$887$	3.87171	+	3.87171i	0.129999	+	0.129999i	−0.639113	+	0.769113i	$0.720699\pi$
$888$	17.1403	−	6.31037i	0.575191	−	0.211762i
$889$	−3.26661			−0.109558
$890$	−15.7411	−	46.8829i	−0.527644	−	1.57152i
$891$	19.2939	−	19.2939i	0.646369	−	0.646369i
$892$	0.323627	−	12.1517i	0.0108358	−	0.406868i
$893$		−	11.5053i		−	0.385009i
$894$	26.1275	−	10.4171i	0.873834	−	0.348399i
$895$	−49.2441	−	2.73378i	−1.64605	−	0.0913801i
$896$	34.0076	+	17.9601i	1.13611	+	0.600005i
$897$	−13.0144	−	13.0144i	−0.434539	−	0.434539i
$898$	−16.0923	+	37.4328i	−0.537006	+	1.24915i
$899$	−6.54516	+	6.54516i	−0.218293	+	0.218293i
$900$	−27.9936	+	21.1863i	−0.933120	+	0.706211i
$901$	0.0971768	+	0.0971768i	0.00323743	+	0.00323743i
$902$	3.38843	+	8.49868i	0.112822	+	0.282975i
$903$	23.5885	−	23.5885i	0.784975	−	0.784975i
$904$	31.7962	+	14.6840i	1.05752	+	0.488384i
$905$	−0.523580	+	9.43136i	−0.0174044	+	0.313509i
$906$	−13.7121	−	5.89479i	−0.455553	−	0.195841i
$907$	26.2062			0.870163			0.435081	−	0.900391i	$-0.356720\pi$
$907$	26.2062			0.870163			0.435081	+	0.900391i	$0.356720\pi$
$908$	−42.2388	+	40.0473i	−1.40174	+	1.32902i
$909$	22.3667	+	22.3667i	0.741856	+	0.741856i
$910$	23.1161	+	11.4952i	0.766292	+	0.381062i
$911$			24.2898i			0.804757i	0.915473	+	0.402378i	$0.131816\pi$
$911$			24.2898i			0.804757i	−0.915473	+	0.402378i	$0.868184\pi$
$912$	−25.7848	−	28.6884i	−0.853820	−	0.949966i
$913$	−29.7983	+	29.7983i	−0.986181	+	0.986181i
$914$	35.6049	−	14.1957i	1.17771	−	0.469553i
$915$	−82.5089	−	4.58047i	−2.72766	−	0.151426i
$916$	−51.8564	−	1.38106i	−1.71339	−	0.0456314i
$917$		−	26.1452i		−	0.863391i
$918$	−0.0724433	−	0.181698i	−0.00239099	−	0.00599694i
$919$		−	41.1294i		−	1.35673i	−0.734723	−	0.678367i	$-0.762688\pi$
$919$		−	41.1294i		−	1.35673i	0.734723	−	0.678367i	$-0.237312\pi$
$920$	−5.56455	−	18.1621i	−0.183458	−	0.598787i
$921$			16.8629i			0.555650i
$922$	−8.23420	+	3.28298i	−0.271179	+	0.108119i
$923$			5.45944i			0.179700i
$924$	45.1874	+	47.6601i	1.48656	+	1.56790i
$925$	12.5763	+	1.40066i	0.413508	+	0.0460535i
$926$	−14.9265	−	37.4377i	−0.490514	−	1.23028i
$927$	−6.80006	+	6.80006i	−0.223343	+	0.223343i
$928$	−29.9946	+	10.1445i	−0.984620	+	0.333009i
$929$		−	43.4799i		−	1.42653i	−0.700894	−	0.713265i	$-0.747215\pi$
$929$		−	43.4799i		−	1.42653i	0.700894	−	0.713265i	$-0.252785\pi$
$930$	12.6493	−	4.24708i	0.414788	−	0.139267i
$931$	12.1734	+	12.1734i	0.398968	+	0.398968i
$932$	−0.110439	+	4.14680i	−0.00361754	+	0.135833i
$933$	1.54653			0.0506313
$934$	−2.17752	+	5.06521i	−0.0712507	+	0.165739i
$935$	0.599188	+	0.669626i	0.0195955	+	0.0218991i
$936$	22.3792	−	8.23911i	0.731487	−	0.269304i
$937$	13.0565	−	13.0565i	0.426537	−	0.426537i	−0.460910	−	0.887447i	$-0.652477\pi$
$937$	13.0565	−	13.0565i	0.426537	−	0.426537i	0.887447	+	0.460910i	$0.152477\pi$
$938$	−47.4370	+	18.9132i	−1.54887	+	0.617537i
$939$	−49.4266	−	49.4266i	−1.61298	−	1.61298i
$940$	8.80516	+	10.3838i	0.287193	+	0.338683i
$941$	−5.53494	+	5.53494i	−0.180434	+	0.180434i	−0.791545	−	0.611111i	$-0.790723\pi$
$941$	−5.53494	+	5.53494i	−0.180434	+	0.180434i	0.611111	+	0.791545i	$0.290723\pi$
$942$	67.1982	+	28.8884i	2.18944	+	0.941235i
$943$	3.62911	+	3.62911i	0.118180	+	0.118180i
$944$	−22.2821	+	20.0270i	−0.725222	+	0.651822i
$945$	0.549030	−	9.88979i	0.0178599	−	0.321715i
$946$	7.62627	+	19.1278i	0.247951	+	0.621898i
$947$		−	31.6905i		−	1.02980i	−0.857249	−	0.514902i	$-0.827828\pi$
$947$		−	31.6905i		−	1.02980i	0.857249	−	0.514902i	$-0.172172\pi$
$948$	30.5688	+	32.2416i	0.992830	+	1.04716i
$949$	23.9947	−	23.9947i	0.778900	−	0.778900i
$950$	−7.08861	−	25.7663i	−0.229985	−	0.835969i
$951$	17.9717			0.582772
$952$	−0.957692	+	0.352583i	−0.0310390	+	0.0114273i
$953$	2.85543	+	2.85543i	0.0924965	+	0.0924965i	0.751841	−	0.659344i	$-0.229166\pi$
$953$	2.85543	+	2.85543i	0.0924965	+	0.0924965i	−0.659344	+	0.751841i	$0.729166\pi$
$954$	5.90568	+	2.53884i	0.191204	+	0.0821981i
$955$	−10.7841	+	9.64970i	−0.348964	+	0.312257i
$956$	17.2602	+	18.2047i	0.558235	+	0.588783i
$957$	−54.0722			−1.74791
$958$	−12.8014	−	5.50331i	−0.413595	−	0.177804i
$959$	−35.9348			−1.16039
$960$	45.2272	+	6.15851i	1.45970	+	0.198765i
$961$	28.2654			0.911786
$962$	−7.89694	−	3.39488i	−0.254608	−	0.109455i
$963$	24.4969			0.789401
$964$	20.4854	+	21.6064i	0.659790	+	0.695895i
$965$	−35.0886	−	1.94793i	−1.12954	−	0.0627062i
$966$	33.8465	+	14.5506i	1.08899	+	0.468156i
$967$	−40.1144	−	40.1144i	−1.28999	−	1.28999i	−0.934790	−	0.355202i	$-0.884412\pi$
$967$	−40.1144	−	40.1144i	−1.28999	−	1.28999i	−0.355202	−	0.934790i	$-0.615588\pi$
$968$	−8.84771	+	3.25737i	−0.284376	+	0.104696i
$969$	1.02356			0.0328816
$970$	9.96981	−	20.0486i	0.320111	−	0.643723i
$971$	−17.3439	+	17.3439i	−0.556592	+	0.556592i	−0.928335	−	0.371743i	$-0.878760\pi$
$971$	−17.3439	+	17.3439i	−0.556592	+	0.556592i	0.371743	+	0.928335i	$0.378760\pi$
$972$	30.6848	+	32.3639i	0.984214	+	1.03807i
$973$		−	55.4322i		−	1.77708i
$974$	10.3079	+	25.8536i	0.330285	+	0.828404i
$975$	30.4519	+	3.39151i	0.975241	+	0.108615i
$976$	38.7267	+	43.0876i	1.23961	+	1.37920i
$977$	−12.2234	−	12.2234i	−0.391060	−	0.391060i	0.484005	−	0.875065i	$-0.339182\pi$
$977$	−12.2234	−	12.2234i	−0.391060	−	0.391060i	−0.875065	+	0.484005i	$0.839182\pi$
$978$	−43.7055	−	18.7889i	−1.39755	−	0.600804i
$979$	−41.8667	+	41.8667i	−1.33807	+	1.33807i
$980$	−20.3034	−	1.67034i	−0.648568	−	0.0533569i
$981$	0.975089	+	0.975089i	0.0311322	+	0.0311322i
$982$	−4.44406	+	1.77185i	−0.141816	+	0.0565421i
$983$	13.6091	−	13.6091i	0.434063	−	0.434063i	−0.455945	−	0.890008i	$-0.650699\pi$
$983$	13.6091	−	13.6091i	0.434063	−	0.434063i	0.890008	+	0.455945i	$0.150699\pi$
$984$	−11.5732	+	4.26079i	−0.368940	+	0.135829i
$985$	41.8132	−	37.4148i	1.33228	−	1.19214i
$986$	0.331843	−	0.771911i	0.0105680	−	0.0245827i
$987$	−26.4053			−0.840491
$988$	−0.483284	+	18.1465i	−0.0153753	+	0.577317i
$989$	8.16797	+	8.16797i	0.259726	+	0.259726i
$990$	37.6344	+	18.7149i	1.19610	+	0.594797i
$991$		−	52.9400i		−	1.68169i	−0.541273	−	0.840847i	$-0.682058\pi$
$991$		−	52.9400i		−	1.68169i	0.541273	−	0.840847i	$-0.317942\pi$
$992$	−8.38525	−	4.14678i	−0.266232	−	0.131660i
$993$	33.7513	−	33.7513i	1.07107	−	1.07107i
$994$	−4.04725	−	10.1511i	−0.128371	−	0.321973i
$995$	31.2573	−	27.9693i	0.990923	−	0.886688i
$996$	−39.0827	−	41.2213i	−1.23838	−	1.30615i
$997$			3.67381i			0.116351i	0.998306	+	0.0581754i	$0.0185283\pi$
$997$			3.67381i			0.116351i	−0.998306	+	0.0581754i	$0.981472\pi$
$998$	18.3370	−	7.31097i	0.580446	−	0.231425i
$999$			3.29792i			0.104342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.s.b.27.2	yes	18
3.2	odd	2		720.2.z.g.667.8		18
4.3	odd	2		320.2.s.b.207.8		18
5.2	odd	4		400.2.j.d.43.6		18
5.3	odd	4		80.2.j.b.43.4	✓	18
5.4	even	2		400.2.s.d.107.8		18
8.3	odd	2		640.2.s.c.287.2		18
8.5	even	2		640.2.s.d.287.8		18
15.8	even	4		720.2.bd.g.523.6		18
16.3	odd	4		80.2.j.b.67.4	yes	18
16.5	even	4		640.2.j.c.607.8		18
16.11	odd	4		640.2.j.d.607.2		18
16.13	even	4		320.2.j.b.47.2		18
20.3	even	4		320.2.j.b.143.8		18
20.7	even	4		1600.2.j.d.143.2		18
20.19	odd	2		1600.2.s.d.207.2		18
40.3	even	4		640.2.j.c.543.2		18
40.13	odd	4		640.2.j.d.543.8		18
48.35	even	4		720.2.bd.g.307.6		18
80.3	even	4	inner	80.2.s.b.3.2	yes	18
80.13	odd	4		320.2.s.b.303.8		18
80.19	odd	4		400.2.j.d.307.6		18
80.29	even	4		1600.2.j.d.1007.8		18
80.43	even	4		640.2.s.d.223.8		18
80.53	odd	4		640.2.s.c.223.2		18
80.67	even	4		400.2.s.d.243.8		18
80.77	odd	4		1600.2.s.d.943.2		18
240.83	odd	4		720.2.z.g.163.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.4	✓	18	5.3	odd	4
80.2.j.b.67.4	yes	18	16.3	odd	4
80.2.s.b.3.2	yes	18	80.3	even	4	inner
80.2.s.b.27.2	yes	18	1.1	even	1	trivial
320.2.j.b.47.2		18	16.13	even	4
320.2.j.b.143.8		18	20.3	even	4
320.2.s.b.207.8		18	4.3	odd	2
320.2.s.b.303.8		18	80.13	odd	4
400.2.j.d.43.6		18	5.2	odd	4
400.2.j.d.307.6		18	80.19	odd	4
400.2.s.d.107.8		18	5.4	even	2
400.2.s.d.243.8		18	80.67	even	4
640.2.j.c.543.2		18	40.3	even	4
640.2.j.c.607.8		18	16.5	even	4
640.2.j.d.543.8		18	40.13	odd	4
640.2.j.d.607.2		18	16.11	odd	4
640.2.s.c.223.2		18	80.53	odd	4
640.2.s.c.287.2		18	8.3	odd	2
640.2.s.d.223.8		18	80.43	even	4
640.2.s.d.287.8		18	8.5	even	2
720.2.z.g.163.8		18	240.83	odd	4
720.2.z.g.667.8		18	3.2	odd	2
720.2.bd.g.307.6		18	48.35	even	4
720.2.bd.g.523.6		18	15.8	even	4
1600.2.j.d.143.2		18	20.7	even	4
1600.2.j.d.1007.8		18	80.29	even	4
1600.2.s.d.207.2		18	20.19	odd	2
1600.2.s.d.943.2		18	80.77	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29924 - 0.558542i) q^{2} -2.55161 q^{3} +(1.37606 + 1.45136i) q^{4} +(1.49107 + 1.66635i) q^{5} +(3.31516 + 1.42518i) q^{6} +(2.40368 + 2.40368i) q^{7} +(-0.977191 - 2.65426i) q^{8} +3.51070 q^{9} +O(q^{10})\)	\(q+(-1.29924 - 0.558542i) q^{2} -2.55161 q^{3} +(1.37606 + 1.45136i) q^{4} +(1.49107 + 1.66635i) q^{5} +(3.31516 + 1.42518i) q^{6} +(2.40368 + 2.40368i) q^{7} +(-0.977191 - 2.65426i) q^{8} +3.51070 q^{9} +(-1.00653 - 2.99782i) q^{10} +(-2.67707 + 2.67707i) q^{11} +(-3.51117 - 3.70331i) q^{12} +2.40164i q^{13} +(-1.78040 - 4.46551i) q^{14} +(-3.80462 - 4.25187i) q^{15} +(-0.212908 + 3.99433i) q^{16} +(-0.0750544 - 0.0750544i) q^{17} +(-4.56125 - 1.96087i) q^{18} +(2.67236 - 2.67236i) q^{19} +(-0.366678 + 4.45708i) q^{20} +(-6.13324 - 6.13324i) q^{21} +(4.97342 - 1.98291i) q^{22} +(2.12375 - 2.12375i) q^{23} +(2.49341 + 6.77263i) q^{24} +(-0.553442 + 4.96928i) q^{25} +(1.34141 - 3.12031i) q^{26} -1.30310 q^{27} +(-0.180999 + 6.79621i) q^{28} +(-3.95795 - 3.95795i) q^{29} +(2.56827 + 7.64925i) q^{30} -1.65367i q^{31} +(2.50762 - 5.07068i) q^{32} +(6.83083 - 6.83083i) q^{33} +(0.0555929 + 0.139435i) q^{34} +(-0.421324 + 7.58941i) q^{35} +(4.83094 + 5.09530i) q^{36} -2.53082i q^{37} +(-4.96467 + 1.97942i) q^{38} -6.12803i q^{39} +(2.96587 - 5.58602i) q^{40} +1.70882i q^{41} +(4.54289 + 11.3942i) q^{42} +3.84601i q^{43} +(-7.56921 - 0.201586i) q^{44} +(5.23469 + 5.85005i) q^{45} +(-3.94547 + 1.57306i) q^{46} +(2.15264 - 2.15264i) q^{47} +(0.543256 - 10.1920i) q^{48} +4.55532i q^{49} +(3.49460 - 6.14717i) q^{50} +(0.191509 + 0.191509i) q^{51} +(-3.48565 + 3.30480i) q^{52} -1.29475 q^{53} +(1.69305 + 0.727839i) q^{54} +(-8.45262 - 0.469246i) q^{55} +(4.03113 - 8.72883i) q^{56} +(-6.81881 + 6.81881i) q^{57} +(2.93166 + 7.35302i) q^{58} +(5.29614 + 5.29614i) q^{59} +(0.935619 - 11.3727i) q^{60} +(10.2413 - 10.2413i) q^{61} +(-0.923645 + 2.14852i) q^{62} +(8.43858 + 8.43858i) q^{63} +(-6.09020 + 5.18744i) q^{64} +(-4.00197 + 3.58100i) q^{65} +(-12.6902 + 5.05960i) q^{66} -10.6230i q^{67} +(0.00565167 - 0.212211i) q^{68} +(-5.41898 + 5.41898i) q^{69} +(4.78640 - 9.62515i) q^{70} +2.27322 q^{71} +(-3.43062 - 9.31831i) q^{72} +(-9.99096 - 9.99096i) q^{73} +(-1.41357 + 3.28815i) q^{74} +(1.41217 - 12.6796i) q^{75} +(7.55589 + 0.201231i) q^{76} -12.8696 q^{77} +(-3.42276 + 7.96180i) q^{78} -8.70617 q^{79} +(-6.97341 + 5.60103i) q^{80} -7.20709 q^{81} +(0.954448 - 2.22017i) q^{82} +11.1310 q^{83} +(0.461838 - 17.3413i) q^{84} +(0.0131558 - 0.236978i) q^{85} +(2.14816 - 4.99689i) q^{86} +(10.0991 + 10.0991i) q^{87} +(9.72165 + 4.48963i) q^{88} +15.6390 q^{89} +(-3.53363 - 10.5244i) q^{90} +(-5.77276 + 5.77276i) q^{91} +(6.00475 + 0.159920i) q^{92} +4.21952i q^{93} +(-3.99914 + 1.59446i) q^{94} +(8.43775 + 0.468420i) q^{95} +(-6.39846 + 12.9384i) q^{96} +(5.00672 + 5.00672i) q^{97} +(2.54434 - 5.91846i) q^{98} +(-9.39839 + 9.39839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9	\( 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} - 20 q^{15} - 6 q^{17} - 24 q^{18} - 2 q^{19} - 12 q^{20} - 16 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25} - 16 q^{26} - 24 q^{27} + 40 q^{28} + 14 q^{29} + 40 q^{30} + 20 q^{32} - 8 q^{33} + 28 q^{34} + 2 q^{35} - 4 q^{36} + 24 q^{38} + 44 q^{40} + 8 q^{42} - 44 q^{44} - 14 q^{45} + 12 q^{46} + 38 q^{47} + 4 q^{48} - 8 q^{50} + 8 q^{51} + 8 q^{52} + 12 q^{53} + 4 q^{54} - 6 q^{55} + 20 q^{56} - 24 q^{57} + 20 q^{58} + 10 q^{59} + 8 q^{60} + 14 q^{61} - 40 q^{62} - 6 q^{63} + 16 q^{64} + 4 q^{66} - 60 q^{68} - 32 q^{69} - 28 q^{70} + 24 q^{71} - 68 q^{72} - 14 q^{73} - 48 q^{74} + 16 q^{75} - 16 q^{76} - 44 q^{77} - 36 q^{78} - 16 q^{79} - 92 q^{80} + 2 q^{81} + 48 q^{82} + 40 q^{83} + 24 q^{84} + 14 q^{85} - 36 q^{86} + 24 q^{87} - 8 q^{88} + 12 q^{89} - 8 q^{90} - 8 q^{92} - 28 q^{94} + 34 q^{95} - 40 q^{96} + 18 q^{97} - 56 q^{98} + 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 - 20 * q^15 - 6 * q^17 - 24 * q^18 - 2 * q^19 - 12 * q^20 - 16 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 - 16 * q^26 - 24 * q^27 + 40 * q^28 + 14 * q^29 + 40 * q^30 + 20 * q^32 - 8 * q^33 + 28 * q^34 + 2 * q^35 - 4 * q^36 + 24 * q^38 + 44 * q^40 + 8 * q^42 - 44 * q^44 - 14 * q^45 + 12 * q^46 + 38 * q^47 + 4 * q^48 - 8 * q^50 + 8 * q^51 + 8 * q^52 + 12 * q^53 + 4 * q^54 - 6 * q^55 + 20 * q^56 - 24 * q^57 + 20 * q^58 + 10 * q^59 + 8 * q^60 + 14 * q^61 - 40 * q^62 - 6 * q^63 + 16 * q^64 + 4 * q^66 - 60 * q^68 - 32 * q^69 - 28 * q^70 + 24 * q^71 - 68 * q^72 - 14 * q^73 - 48 * q^74 + 16 * q^75 - 16 * q^76 - 44 * q^77 - 36 * q^78 - 16 * q^79 - 92 * q^80 + 2 * q^81 + 48 * q^82 + 40 * q^83 + 24 * q^84 + 14 * q^85 - 36 * q^86 + 24 * q^87 - 8 * q^88 + 12 * q^89 - 8 * q^90 - 8 * q^92 - 28 * q^94 + 34 * q^95 - 40 * q^96 + 18 * q^97 - 56 * q^98 + 22 * q^99

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